long correlations and levy models applied to the study of memory effects in high frequency tick data abstract this work is devoted to the study of long correlations memory effects and other statistical properties of high frequency tick data we use a sample of 25 stocks for this purpose we verify that the behavior of the return is compatible with that of continuous time levy processes we also study the presence of memory effects and long range correlations in the values of the return

pricing geometric asian rainbow options under the mixed fractional brownian motion abstract we deal with the pricing of geometric asian rainbow options under the mixed fractional brownian motion based on standard no arbitrage arguments we obtain a partial differential problem in several independent variables which we solve by employing suitable changes of variables and analytical results derived in bos and ware 2001 and stulz 1982b numerical test cases are presented in which the pricing formula obtained is applied to geometric asian rainbow options on two and three underlying assets monte carlo simulations are also performed which confirm the correctness of the proposed closed form solution

spectral gmm estimation of continuous time processes abstract this paper derives a methodology for the estimation of continuous time stochastic models based on the characteristic function the estimation method does not require discretization of the stochastic process and it is simple to apply in practice the method is essentially generalized method of moments on the complex plane hence it shares the efficiency and distribution properties of gmm estimators we illustrate the method with some applications to relevant estimation problems in continuous time finance we estimate a model of stochastic volatility a jump diffusion model with constant volatility and a model that nests both the stochastic volatility model and the jump diffusion model we find that negative jumps are important to explain skewness and asymmetry in excess kurtosis of the stock return distribution while stochastic volatility is important to capture the overall level of this kurtosis positive jumps are not statistically significant once we allow for stochastic volatility in the model we also estimate a non affine model of stochastic volatility and find that the power of the diffusion coefficient appears to be between one and two rather than the value of one half that leads to the standard affine stochastic volatility model however we find that including jumps into this non affine stochastic volatility model reduces the power of the diffusion coefficient to one half finally we offer an explanation for the observation that the estimate of persistence in stochastic volatility increases dramatically as the frequency of the observed data falls based on a multiple factor stochastic volatility model

efficient implementation of markov chain monte carlo when using an unbiased likelihood estimator summary when an unbiased estimator of the likelihood is used within a metropolis hastings chain it is necessary to trade off the number of monte carlo samples used to construct this estimator against the asymptotic variances of the averages computed under this chain using many monte carlo samples will typically result in metropolis hastings averages with lower asymptotic variances than the corresponding averages that use fewer samples however the computing time required to construct the likelihood estimator increases with the number of samples under the assumption that the distribution of the additive noise introduced by the loglikelihood estimator is gaussian with variance inversely proportional to the number of samples and independent of the parameter value at which it is evaluated we provide guidelines on the number of samples to select we illustrate our results by considering a stochastic volatility model applied to stock index returns

on the shape of a tridiagonal pair abstract let k denote a field and let v denote a vector space over k with finite positive dimension we consider a pair of linear transformations a v v and a v v that satisfy the following conditions i each of a a is diagonalizable ii there exists an ordering v i i 0 d of the eigenspaces of a such that a v i v i 1 v i v i 1 for 0 i d where v 1 0 and v d 1 0 iii there exists an ordering v i i 0 of the eigenspaces of a such that av i v i 1 v i v i 1 for 0 i where v 1 0 and v 1 0 iv there is no subspace w of v such that aw w a w w w 0 w v we call such a pair a tridiagonal pair on v it is known that d and for 0 i d the dimensions of v i v i v d i v d i coincide we denote this common dimension by i in this paper we prove that i 0 d i for 0 i d it is already known that 0 1 if k is algebraically closed

a systolic realization for 2 d digital filters systolic hardware realizations for two dimensional finite impulse response fir and infinite impulse response iir digital filters are presented the structure permits the 2 d input data to be scanned row wise and broadcasted one value at a time to various processing elements shift registers are used to store the required data needed by the 2 d recursive equation a processing element can be implemented in vlsi and as many of these as are required to satisfy the order of the filter can be used to build the total structure

threshold bipower variation and the impact of jumps on volatility forecasting this study reconsiders the role of jumps for volatility forecasting by showing that jumps have a positive and mostly significant impact on future volatility this result becomes apparent once volatility is separated into its continuous and discontinuous components using estimators which are not only consistent but also scarcely plagued by small sample bias with the aim of achieving this we introduce the concept of threshold bipower variation which is based on the joint use of bipower variation and threshold estimation we show that its generalization threshold multipower variation admits a feasible central limit theorem in the presence of jumps and provides less biased estimates with respect to the standard multipower variation of the continuous quadratic variation in finite samples we further provide a new test for jump detection which has substantially more power than tests based on multipower variation empirical analysis on the s p500 index individual stocks and us bond yields shows that the proposed techniques improve significantly the accuracy of volatility forecasts especially in periods following the occurrence of a jump

numerically pricing american options under the generalized mixed fractional brownian motion model abstract in this paper we introduce a robust numerical method based on the upwind scheme for the pricing of american puts under the generalized mixed fractional brownian motion gmfbm model by using portfolio analysis and applying the wick ito formula a partial differential equation pde governing the prices of vanilla options under the gmfbm is successfully derived for the first time based on this we formulate the pricing of american puts under the current model as a linear complementarity problem lcp unlike the classical black scholes b s model or the generalized b s model discussed in cen and le 2011 the newly obtained lcp under the gmfbm model is difficult to be solved accurately because of the numerical instability which results from the degeneration of the governing pde as time approaches zero to overcome this difficulty a numerical approach based on the upwind scheme is adopted it is shown that the coefficient matrix of the current method is an m matrix which ensures its stability in the maximum norm sense remarkably we have managed to provide a sharp theoretic error estimate for the current method which is further verified numerically the results of various numerical experiments also suggest that this new approach is quite accurate and can be easily extended to price other types of financial derivatives with an american style exercise feature under the gmfbm model

bootstrapping realized volatility we propose bootstrap methods for a general class of nonlinear transformations of realized volatility which includes the raw version of realized volatility and its logarithmic transformation as special cases we consider the independent and identically distributed i i d bootstrap and the wild bootstrap wb and prove their first order asymptotic validity under general assumptions on the log price process that allow for drift and leverage effects we derive edgeworth expansions in a simpler model that rules out these effects the i i d bootstrap provides a second order asymptotic refinement when volatility is constant but not otherwise the wb yields a second order asymptotic refinement under stochastic volatility provided we choose the external random variable used to construct the wb data appropriately none of these methods provides third order asymptotic refinements both methods improve upon the first order asymptotic theory in finite samples

a classification of sharp tridiagonal pairs let f denote a field and let v denote a vector space over f with finite positive dimension we consider a pair of linear transformations a v v and a v v that satisfy the following conditions i each of a a is diagonalizable ii there exists an ordering vi i 0d of the eigenspaces of a such that a vi vi 1 vi vi 1 for 0 i d where v 1 0 and vd 1 0 iii there exists an ordering vi i 0 of the eigenspaces of a such that avi vi 1 vi vi 1 for 0 i where v 1 0 and v 1 0 iv there is no subspace w of v such that aw w a w w w 0 w v we call such a pair a tridiagonal pair on v it is known that d and for 0 i d the dimensions of vi vd i vi vd i coincide the pair a a is called sharp whenever dimv0 1 it is known that if f is algebraically closed then a a is sharp in this paper we classify up to isomorphism the sharp tridiagonal pairs as a corollary we classify up to isomorphism the tridiagonal pairs over an algebraically closed field we obtain these classifications by proving the conjecture

pricing formula for european currency option and exchange option in a generalized jump mixed fractional brownian motion with time varying coefficients abstract in this paper a new framework for pricing the european currency option is developed in the case where the spot exchange rate follows a generalized mixed fractional brownian motion with jumps hereafter gjmfbm in addition we consider a general case that the coefficients of the model are time varying to capture the behaviors of exchange rate the combination of poisson jumps and generalized mixed fractional brownian motion is introduced to derive the pricing formula for some options we firstly derive a generalized mixed fractional girsanov theorem and some results regarding the quasi conditional expectation that we will need for the rest of the paper then analytic pricing formulas for european currency option and exchange option are obtained using the equivalent martingale measure finally through some numerical experiments and discussion we show that the gjmfbm model is different with the other previous ones

two linear transformations each tridiagonal with respect to an eigenbasis of the other let k denote a field and let v denote a vector space over k with finite positive dimension we consider a pair of linear transformations a v v and a v v satisfying both conditions below 1 i there exists a basis for v with respect to which the matrix representing a is diagonal and the matrix representing a is irreducible tridiagonal 2 ii there exists a basis for v with respect to which the matrix representing a is diagonal and the matrix representing a is irreducible tridiagonal we call such a pair a leonard pair on v refining this notion a bit we introduce the concept of a leonard system we give a complete classification of leonard systems integral to our proof is the following result we show that for any leonard pair a a on v there exists a sequence of scalars taken from k such that both 0 a a2a aa a a a2 aa a a a 0 a a 2a a aa aa 2 a a aa a where r s means rs sr the sequence is uniquely determined by the leonard pair if the dimension of v is at least 4 we conclude by showing how leonard systems correspond to q racah and related polynomials from the askey scheme

exact simulation of stochastic volatility and other affine jump diffusion processes the stochastic differential equations for affine jump diffusion models do not yield exact solutions that can be directly simulated discretization methods can be used for simulating security prices under these models however discretization introduces bias into the simulation results and a large number of time steps may be needed to reduce the discretization bias to an acceptable level this paper suggests a method for the exact simulation of the stock price and variance under hestons stochastic volatility model and other affine jump diffusion processes the sample stock price and variance from the exact distribution can then be used to generate an unbiased estimator of the price of a derivative security we compare our method with the more conventional euler discretization method and demonstrate the faster convergence rate of the error in our method specifically our method achieves an o s 1 2 convergence rate where s is the total computational budget the convergence rate for the euler discretization method is o s 1 3 or slower depending on the model coefficients and option payoff function

financial asset returns direction of change forecasting and volatility dynamics we consider three sets of phenomena that feature prominently in the financial economics literature 1 conditional mean dependence or lack thereof in asset returns 2 dependence and hence forecastability in asset return signs and 3 dependence and hence forecastability in asset return volatilities we show that they are very much interrelated and explore the relationships in detail among other things we show that 1 volatility dependence produces sign dependence so long as expected returns are nonzero so that one should expect sign dependence given the overwhelming evidence of volatility dependence 2 it is statistically possible to have sign dependence without conditional mean dependence 3 sign dependence is not likely to be found via analysis of sign autocorrelations runs tests or traditional market timing tests because of the special nonlinear nature of sign dependence so that traditional market timing tests are best viewed as tests for sign dependence arising from variation in expected returns rather than from variation in volatility or higher moments 4 sign dependence is not likely to be found in very high frequency e g daily or very low frequency e g annual returns instead it is more likely to be found at intermediate return horizons and 5 the link between volatility dependence and sign dependence remains intact in conditionally non gaussian environments for example with time varying conditional skewness and or kurtosis

time dependent hurst exponent in financial time series abstract we calculate the hurst exponent h t of several time series by dynamical implementation of a recently proposed scaling technique the detrending moving average dma in order to assess the accuracy of the technique we calculate the exponent h t for artificial series simulating monofractal brownian paths with assigned hurst exponents h we next calculate the exponent h t for the return of high frequency tick by tick sampled every minute series of the german market we find a much more pronounced time variability in the local scaling exponent of financial series compared to the artificial ones the dma algorithm allows the calculation of the exponent h t without any a priori assumption on the stochastic process and on the probability distribution function of the random variables as happens for example in the case of the kitagawa grid and the extended kalmann filtering methods the present technique examines the local scaling exponent h t around a given instant of time this is a significant advance with respect to the standard wavelet transform or to the higher order power spectrum technique which instead operate on the global properties of the series by legendre or fourier transform of qth order moments

quantifying and modeling long range cross correlations in multiple time series with applications to world stock indices we propose a modified time lag random matrix theory in order to study time lag cross correlations in multiple time series we apply the method to 48 world indices one for each of 48 different countries we find long range power law cross correlations in the absolute values of returns that quantify risk and find that they decay much more slowly than cross correlations between the returns the magnitude of the cross correlations constitutes bad news for international investment managers who may believe that risk is reduced by diversifying across countries we find that when a market shock is transmitted around the world the risk decays very slowly we explain these time lag cross correlations by introducing a global factor model gfm in which all index returns fluctuate in response to a single global factor for each pair of individual time series of returns the cross correlations between returns or magnitudes can be modeled with the autocorrelations of the global factor returns or magnitudes we estimate the global factor using principal component analysis which minimizes the variance of the residuals after removing the global trend using random matrix theory a significant fraction of the world index cross correlations can be explained by the global factor which supports the utility of the gfm we demonstrate applications of the gfm in forecasting risks at the world level and infinding uncorrelated individual indices we find ten indices that are practically uncorrelated with the global factor and with the remainder of the world indices which is relevant information for world managers in reducing their portfolio risk finally we argue that this general method can be applied to a wide range of phenomena in which time series are measured ranging from seismology and physiology to atmospheric geophysics

a reduced form framework for modeling volatility of speculative prices based on realized variation measures abstract building on realized variance and bipower variation measures constructed from high frequency financial prices we propose a simple reduced form framework for effectively incorporating intraday data into the modeling of daily return volatility we decompose the total daily return variability into the continuous sample path variance the variation arising from discontinuous jumps that occur during the trading day as well as the overnight return variance our empirical results based on long samples of high frequency equity and bond futures returns suggest that the dynamic dependencies in the daily continuous sample path variability are well described by an approximate long memory har garch model while the overnight returns may be modeled by an augmented garch type structure the dynamic dependencies in the non parametrically identified significant jumps appear to be well described by the combination of an ach model for the time varying jump intensities coupled with a relatively simple log linear structure for the jump sizes finally we discuss how the resulting reduced form model structure for each of the three components may be used in the construction of out of sample forecasts for the total return volatility

a monte carlo simulation to the performance of the r s and v s methods statistical revisit and real world application abstract a correct or precise estimation of the hurst exponent is one of the fundamentally important problems in the financial economics literature there are three widely used tools to estimate the hurst exponent the canonical rescaled range r s the variance rescaled statistic v s and the modified rescaled range modified r s to clarify their performance we compare them by monte carlo simulations we generate many time series of a fractal brownian motion of a weierstrass mandelbrot cosine fractal function and of a fractionally integrated process whose theoretical hurst exponents are known to compare the hurst exponents estimated by the three methods to better understand their pragmatic performance we further apply all of these methods empirically in real world applications our results imply it is not appropriate to conclude simply which method is better as v s performs better when the analyzed market is anti persistent while r s seems to be a reliable tool used in persistent market

increased correlation among asset classes are volatility or jumps to blame or both abstract we develop estimators and asymptotic theory to decompose the quadratic covariation between two assets into its continuous and jump components in a manner that is robust to the presence of market microstructure noise using high frequency data on different assets classes we find that the recent financial crisis led to an increase in both the quadratic variations of the assets and their correlations however we find little evidence to suggest a change between the relative contributions of the brownian and jump components as both comove co jumps stem from surprising news announcements that occur primarily before the opening of the us market and are also accompanied by an increase in brownian driven correlations

smc 2 an efficient algorithm for sequential analysis of state space models we consider the generic problem of performing sequential bayesian inference in a state space model with observation process y state process x and fixed parameter theta an idealized approach would be to apply the iterated batch importance sampling ibis algorithm of chopin 2002 this is a sequential monte carlo algorithm in the theta dimension that samples values of theta reweights iteratively these values using the likelihood increments p y t y 1 t 1 theta and rejuvenates the theta particles through a resampling step and a mcmc update step in state space models these likelihood increments are intractable in most cases but they may be unbiasedly estimated by a particle filter in the x dimension for any fixed theta this motivates the smc 2 algorithm proposed in this article a sequential monte carlo algorithm defined in the theta dimension which propagates and resamples many particle filters in the x dimension the filters in the x dimension are an example of the random weight particle filter as in fearnhead et al 2010 on the other hand the particle markov chain monte carlo pmcmc framework developed in andrieu et al 2010 allows us to design appropriate mcmc rejuvenation steps thus the theta particles target the correct posterior distribution at each iteration t despite the intractability of the likelihood increments we explore the applicability of our algorithm in both sequential and non sequential applications and consider various degrees of freedom as for example increasing dynamically the number of x particles we contrast our approach to various competing methods both conceptually and empirically through a detailed simulation study included here and in a supplement and based on particularly challenging examples

tridiagonal pairs and the q tetrahedron algebra abstract the q tetrahedron algebra q was recently introduced and has been studied in connection with tridiagonal pairs in this paper we further develop this connection let k denote an algebraically closed field and let q denote a nonzero scalar in k that is not a root of unity let v denote a vector space over k with finite positive dimension and let a a denote a tridiagonal pair on v let i i 0 d resp i i 0 d denote a standard ordering of the eigenvalues of a resp a ito and terwilliger have shown that when i q 2 i d and i q d 2 i 0 i d there exists an irreducible q module structure on v such that the q generators x 01 x 23 act as a a respectively in this paper we examine the case in which there exists a nonzero scalar c in k such that i q 2 i d and i q 2 i d cq d 2 i for 0 i d in this case we associate to a a a polynomial p in one variable and prove the following theorem as our main result theorem the following are equivalent 1 i there exists a q module structure on v such that x 01 acts as a and x 30 cx 23 acts as a where x 01 x 30 x 23 are standard generators for q 2 ii p q 2 d 2 q q 1 2 0 suppose i and ii hold then the q module structure on v is unique and irreducible

arbitrage in a discrete version of the wick fractional black scholes market we consider binary market models based on the discrete wick product instead of the pathwise product and provide a sufficient criterion for the existence of an arbitrage this arbitrage is explicitly constructed in the class of self financing one step buy and hold strategies i e the investor holds shares of the stock only at one time step using coefficients obtained from an approximation of a fractional brownian motion with hurst parameter

statistical properties of the volatility of price fluctuations we study the statistical properties of volatility measured by locally averaging over a time window t the absolute value of price changes over a short time interval ensuremath delta t we analyze the s 500 stock index for the 13 year period jan 1984 to dec 1996 we find that the cumulative distribution of the volatility is consistent with a power law asymptotic behavior characterized by an exponent ensuremath mu ensuremath approx 3 similar to what is found for the distribution of price changes the volatility distribution retains the same functional form for a range of values of t further we study the volatility correlations by using the power spectrum analysis both methods support a power law decay of the correlation function and give consistent estimates of the relevant scaling exponents also both methods show the presence of a crossover at approximately 1 5 days in addition we extend these results to the volatility of individual companies by analyzing a data base comprising all trades for the largest 500 u s companies over the two year period jan 1994 to dec 1995

a very efficient approach to compute the first passage probability density function in a time changed brownian model applications in finance abstract we propose a numerical method to compute the first passage probability density function in a time changed brownian model in particular we derive an integral representation of such a density function in which the integrand functions must be obtained solving a system of volterra equations of the first kind in addition we develop an ad hoc numerical procedure to regularize and solve this system of integral equations the proposed method is tested on three application problems of interest in mathematical finance namely the calculation of the survival probability of an indebted firm the pricing of a single knock out put option and the pricing of a double knock out put option the results obtained reveal that the novel approach is extremely accurate and fast and performs significantly better than the finite difference method

bootstrapping realized multivariate volatility measures we study bootstrap methods for statistics that are a function of multivariate high frequency returns such as realized regression coefficients and realized covariances and correlations for these measures of covariation the monte carlo simulation results of barndorff nielsen and shephard 2004 show that finite sample distortions associated with their feasible asymptotic theory approach may arise if sampling is not too frequent this motivates our use of the bootstrap as an alternative tool of inference for covariation measures we consider an i i d bootstrap applied to the vector of returns we show that the finite sample performance of the bootstrap is superior to the existing first order asymptotic theory nevertheless and contrary to the existing results in the bootstrap literature for regression models subject to heteroskedasticity in the error term the edgeworth expansion for the i i d bootstrap that we develop here shows that this method is not second order accurate we argue that this is due to the fact that the conditional mean parameters of realized regression models are heterogeneous under stochastic volatility

stochastic volatility with leverage fast and efficient likelihood inference this paper is concerned with the bayesian analysis of stochastic volatility sv models with leverage specifically the paper shows how the often used kim et al 1998 stochastic volatility likelihood inference and comparison with arch models review of economic studies 65 361 393 method that was developed for sv models without leverage can be extended to models with leverage the approach relies on the novel idea of approximating the joint distribution of the outcome and volatility innovations by a suitably constructed ten component mixture of bivariate normal distributions the resulting posterior distribution is summarized by mcmc methods and the small approximation error in working with the mixture approximation is corrected by a reweighting procedure the overall procedure is fast and highly efficient we illustrate the ideas on daily returns of the tokyo stock price index finally extensions of the method are described for superposition models where the log volatility is made up of a linear combination of heterogenous and independent autoregressions and heavy tailed error distributions student and log normal

integrated variance forecasting model based vs reduced form abstract this paper compares model based and reduced form forecasts of financial volatility when high frequency return data are available we derived exact formulas for the forecast errors and analyzed the contribution of the wrong data modeling and errors in forecast inputs the comparison is made for feasible forecasts i e we assumed that the true data generating process latent states and parameters are unknown as an illustration the same comparison is carried out empirically for spot 5 min returns of dm usd exchange rates it is shown that the comparison between feasible reduced form and model based forecasts is not always in favor of the latter in contrast to their infeasible versions the reduced form approach is generally better for long horizon forecasting and for short horizon forecasting in the presence of microstructure noise

arbitrage with fractional gaussian processes abstract while the arbitrage opportunity in the black scholes model driven by fractional brownian motion has a long history the arbitrage strategy in the black scholes model driven by general fractional gaussian processes is in its infancy the development of stochastic calculus with respect to fractional gaussian processes allowed us to study such models in this paper following the idea of shiryaev 1998 an arbitrage strategy is constructed for the black scholes model driven by fractional gaussian processes when the stochastic integral is interpreted in the riemann stieltjes sense arbitrage opportunities in some fractional gaussian processes including fractional brownian motion sub fractional brownian motion bi fractional brownian motion weighted fractional brownian motion and tempered fractional brownian motion are also investigated

long term memory in stock market prices a test for long term memory that is robust to short range dependence is developed it is a modification of the r s statistic and the relevant asymptotic sampling theory is derived via functional central limit theory contrary to previous findings when applied to daily and monthly stock returns indexes over several time periods this test yields no evidence of long range dependence once short range dependence is accounted for monte carlo experiments show that the modified r s test has power against at least two specific models of long term memory suggesting that models with short range dependence may adequately capture the behavior of historical stock returns copyright 1991 by the econometric society

the structure of a tridiagonal pair let k denote a field and let v denote a vector space over k with finite positive dimension we consider a pair of k linear transformations a v v and a v v that satisfy the following conditions i each of a a is diagonalizable ii there exists an ordering vi i 0d of the eigenspaces of a such that a vi vi 1 vi vi 1 for 0 i d where v 1 0 and vd 1 0 iii there exists an ordering vi i 0 of the eigenspaces of a such that avi vi 1 vi vi 1 for 0 i where v 1 0 and v 1 0 iv there is no subspace w of v such that aw w a w w w 0 w v we call such a pair a tridiagonal pair on v it is known that d and for 0 i d the dimensions of vi vd i vi vd i coincide in this paper we show that the following i iv hold provided that k is algebraically closed i each of v0 v0 vd vd has dimension 1 ii there exists a nondegenerate symmetric bilinear form on v such that au v u av and a u v u a v for all u v v iii there exists a unique anti automorphism of end v that fixes each of a a iv the pair a a is determined up to isomorphism by the data i i 0d i i 0d i i 0d where i resp i is the eigenvalue of a resp a on vi resp vi and i i 0d is the split sequence of a a corresponding to i i 0d and i i 0d

econometric analysis of jump driven stochastic volatility models abstract this paper introduces and studies the econometric properties of a general new class of models which i refer to as jump driven stochastic volatility models in which the volatility is a moving average of past jumps i focus attention on two particular semiparametric classes of jump driven stochastic volatility models in the first the price has a continuous component with time varying volatility and time homogeneous jumps the second jump driven stochastic volatility model analyzed here has only jumps in the price which have time varying size in the empirical application i model the memory of the stochastic variance with a carma 2 1 kernel and set the jumps in the variance to be proportional to the squared price jumps the estimation which is based on matching moments of certain realized power variation statistics calculated from high frequency foreign exchange data shows that the jump driven stochastic volatility model containing continuous component in the price performs best it outperforms a standard two factor affine jump diffusion model but also the pure jump jump driven stochastic volatility model for the particular jump specification

pricing credit default swaps under a multi scale stochastic volatility model abstract in this paper we consider the pricing of credit default swaps cdss with the reference asset driven by a geometric brownian motion with a multi scale stochastic volatility sv which is a two factor volatility process with one factor controlling the fast time scale and the other representing the slow time scale a key feature of the current methodology is to establish an equivalence relationship between the cds and the down and out binary option through the discussion of no default probability while balancing the two sv processes with the perturbation method an approximate but closed form pricing formula for the cds contract is finally obtained whose accuracy is in the order of o

time varying hurst exponent for us stock markets abstract in this work the dynamical behavior of the us stock markets is characterized on the basis of the temporal variations of the hurst exponent estimated with detrended fluctuation analysis dfa over moving windows for the historical dow jones 1928 2007 and the s p 500 1950 2007 daily indices according to the results drawn i the hurst exponent displays an erratic dynamics with some episodes alternating low and high persistent behavior ii the major breakthrough of the long term trend of the scaling behavior occurred in 1972 at the end of the bretton woods system when the hurst exponent shifted form a positive to a negative long term trend other effects such as the 1987 crisis and the emergence of anti correlated behavior in the recent two years are also discussed

neglecting parameter changes in garch models if a garch model is estimated on a time series that contains parameter changes in the conditional volatility process and these parameter changes are not accounted for a distinct error in the estimation occurs the sum of the estimated autoregressive parameters of the conditional variance converges to one in finite samples the sum of the estimated autoregressive parameters is heavily biased towards one this paper shows that this convergence holds for all common estimators of garch simulations of the garch model show that the effect occurs for realistic parameter changes and sample sizes for financial volatility data

pricing currency options in the mixed fractional brownian motion abstract this paper deals with the problem of pricing european currency options in the mixed fractional brownian environment both the pricing formula and the mixed fractional partial differential equation for european call currency options are obtained some greeks and the estimator of volatility are also provided empirical studies and simulation results confirm the theoretical findings and show that the mixed fractional brownian pricing model is a reasonable one

realised quantile based estimation of the integrated variance in this paper we propose a new jump robust quantile based realised variance measure of ex post return variation that can be computed using potentially noisy data the estimator is consistent for the integrated variance and we present feasible central limit theorems which show that it converges at the best attainable rate and has excellent efficiency asymptotically the quantile based realised variance is immune to finite activity jumps and outliers in the price series while in modified form the estimator is applicable with market microstructure noise and therefore operational on high frequency data simulations show that it has superior robustness properties in finite sample while an empirical application illustrates its use on equity data

the fractional and mixed fractional cev model abstract the continuous observation of the financial markets has identified some stylized facts which challenge the conventional assumptions promoting the born of new approaches on the one hand the long range dependence has been faced replacing the traditional gauss wiener process brownian motion characterized by stationary independent increments by a fractional version on the other hand the cev model addresses the leverage effect and smile skew phenomena efficiently in this paper these two insights are merging and both the fractional and mixed fractional extensions for the cev model are developed using the fractional versions of both the ito s calculus and the fokker planck equation the transition probability density function of the asset price is obtained as the solution of a non stationary feller process with time varying coefficients getting an analytical valuation formula for a european call option besides the greeks are computed and compared with the standard case

tridiagonal pairs of shape 1 2 1 abstract let f denote a field and let v denote a vector space over f with finite positive dimension we consider a pair of linear transformations a v v and a v v that satisfies the following conditions i each of a a is diagonalizable ii there exists an ordering v i i 0 d of the eigenspaces of a such that a v i v i 1 v i v i 1 for 0 i d where v 1 0 and v d 1 0 iii there exists an ordering v i i 0 of the eigenspaces of a such that av i v i 1 v i v i 1 for 0 i where v 1 0 and v 1 0 iv there is no subspace w of v such that aw w a w w w 0 w v we call such a pair a tridiagonal pair on v it is known that d and that for 0 i d the dimensions of v i v d i v i v d i coincide we denote this common value by i the sequence i i 0 d is called the shape of the pair in this paper we assume the shape is 1 2 1 and obtain the following results we describe six bases for v one diagonalizes a another diagonalizes a and the other four underlie the split decompositions for a a we give the action of a and a on each basis for each ordered pair of bases among the six we give the transition matrix at the end we classify the tridiagonal pairs of shape 1 2 1 in terms of a sequence of scalars called the parameter array

common scaling patterns in intertrade times of u s stocks we analyze the sequence of time intervals between consecutive stock trades of thirty companies representing eight sectors of the u s economy over a period of 4 yrs for all companies we find that i the probability density function of intertrade times may be fit by a weibull distribution ii when appropriately rescaled the probability densities of all companies collapse onto a single curve implying a universal functional form iii the intertrade times exhibit power law correlated behavior within a trading day and a consistently greater degree of correlation over larger time scales in agreement with the correlation behavior of the absolute price returns for the corresponding company and iv the magnitude series of intertrade time increments is characterized by long range power law correlations suggesting the presence of nonlinear features in the trading dynamics while the sign series is anticorrelated at small scales our results suggest that independent of industry sector market capitalization and average level of trading activity the series of intertrade times exhibit possibly universal scaling patterns which may relate to a common mechanism underlying the trading dynamics of diverse companies further our observation of long range power law correlations and a parallel with the crossover in the scaling of absolute price returns for each individual stock support the hypothesis that the dynamics of transaction times may play a role in the process of price formation

cross correlations between volume change and price change in finance one usually deals not with prices but with growth rates r defined as the difference in logarithm between two consecutive prices here we consider not the trading volume but rather the volume growth rate r the difference in logarithm between two consecutive values of trading volume to this end we use several methods to analyze the properties of volume changes r and their relationship to price changes r we analyze 14 981 daily recordings of the standard and poor s s p 500 index over the 59 year period 1950 2009 and find power law cross correlations between r and r by using detrended cross correlation analysis dcca we introduce a joint stochastic process that models these cross correlations motivated by the relationship between r and r we estimate the tail exponent of the probability density function p r r 1 for both the s p 500 index as well as the collection of 1819 constituents of the new york stock exchange composite index on 17 july 2009 as a new method to estimate we calculate the time intervals q between events where r q we demonstrate that q the average of q obeys q q we find 3 furthermore by aggregating all q values of 28 global financial indices we also observe an approximate inverse cubic law

mock tridiagonal systems we introduce the notion of a mock tridiagonal system this is a generalization of a tridiagonal system in which the irreducibility assumption is replaced by a certain nonvanishing condition we show how mock tridiagonal systems can be used to construct tridiagonal systems that meet certain specifications this paper is part of our ongoing project to classify the tridiagonal systems up to isomorphism

transition maps between the 24 bases for a leonard pair abstract let v denote a vector space with finite positive dimension we consider a pair of linear transformations a v v and a v v that satisfy i and ii below 1 i there exists a basis for v with respect to which the matrix representing a is irreducible tridiagonal and the matrix representing a is diagonal 2 ii there exists a basis for v with respect to which the matrix representing a is irreducible tridiagonal and the matrix representing a is diagonal we call such a pair a leonard pair on v in an earlier paper we described 24 special bases for v one feature of these bases is that with respect to each of them the matrices that represent a and a are i diagonal and irreducible tridiagonal or ii irreducible tridiagonal and diagonal or iii lower bidiagonal and upper bidiagonal or iv upper bidiagonal and lower bidiagonal for each ordered pair of bases among the 24 there exists a unique linear transformation from v to v that sends the first basis to the second basis we call this the transition map in this paper we find each transition map explicitly as a polynomial in a a

a new realization fo 2 d digital filters a systolic array realization for 2 d digital filters is presented it is based on chan s local state space model this structure has the minimum number of states minimum delays a technique is also presented to reduce the number of multipliers to its minimum conditions that the system eigenvalues have to satisfy to ensure low sensitivity with respect to the variations in the multipliers are developed several examples are included to illustrate the proposed techniques

reprojecting partially observed systems with application to interest rate diffusions abstract we introduce reprojection as a general purpose technique for characterizing the dynamic response of a partially observed nonlinear system to its observable history reprojection is the third step of a procedure wherein first data are summarized by projection onto a hermite series representation of the unconstrained transition density for observables second system parameters are estimated by minimum chi squared where the chi squared criterion is a quadratic form in the expected score of the projection and third the constraints on dynamics implied by the nonlinear system are imposed by projecting a long simulation of the estimated system onto a hermite series representation of the constrained transition density for observables the constrained transition density can be used to study the response of the system to its observable history we utilize the technique to assess the dynamics of several diffusion models for the short term interest rate that have been proposed and to compare them to a ne

arch models as diffusion approximations abstract this paper investigates the convergence of stochastic difference equations e g arch to stochastic differential equations as the length of the discrete time intervals between observations goes to zero these results are applied to the garch 1 1 model of bollerslev 1986 and to the ar 1 exponential arch model of nelson 1989 in their continuous time limits the conditional variance processes in these models have stationary distributions that are inverted gamma and lognormal respectively in addition a class of diffusion approximations based on the exponential arch model is developed

stochastic calculus for fractional brownian motion i theory in this paper a stochastic calculus is given for the fractional brownian motions that have the hurst parameter in 1 2 1 a stochastic integral of ito type is defined for a family of integrands so that the integral has zero mean and an explicit expression for the second moment this integral uses the wick product and a derivative in the path space some ito formulae or change of variables formulae are given for smooth functions of a fractional brownian motion or some processes related to a fractional brownian motion a stochastic integral of stratonovich type is defined and the two types of stochastic integrals are explicitly related a square integrable functional of a fractional brownian motion is expressed as an infinite series of orthogonal multiple integrals

bond pricing under mixed generalized cir model with mixed wishart volatility process this paper proposes an extended version of the coxingersollross cir model with stochastic volatility and a pricing method on zero coupon bond under this model in this version we replace the standard brownian motion process with a semi martingale process named the mixed fractional brownian motion mfbm process which is a linear combination of a fractional brownian motion fbm and a standard brownian motion we assume that the part of the volatility process follows a mixed wishart process which defines by the square of the matrix valued mfbm process in order to evaluate the price of the zero coupon bond under the proposed model we use monte carlo simulation method the computed values of the zero coupon bond compare with the other interest rate models

highly molecular systolic structures for denominator separable 2 d recursive filters two systolic realization structures for the implementation of 2 d denominator separable recursive filters are presented these structures possess a high degree of modularity and parallelism with low roundoff noise the number of delays and multipliers is fewer than for similar realizations in the literature the proposed structures are more suitable for special purpose hardware and amenable to vlsi design

exact and asymptotic tests for possibly non regular hypotheses on stochastic volatility models abstract we study the problem of testing hypotheses on the parameters of one and two factor stochastic volatility models sv allowing for the possible presence of non regularities such as singular moment conditions and unidentified parameters which can lead to non standard asymptotic distributions we focus on the development of simulation based exact procedures whose level can be controlled in finite samples as well as on large sample procedures which remain valid under non regular conditions we consider wald type score type and likelihood ratio type tests based on a simple moment estimator which can be easily simulated we also propose a c type test which is very easy to implement and exhibits relatively good size and power properties besides usual linear restrictions on the sv model coefficients the problems studied include testing homoskedasticity against a sv alternative which involves singular moment conditions under the null hypothesis and testing the null hypothesis of one factor driving the dynamics of the volatility process against two factors which raises identification difficulties three ways of implementing the tests based on alternative statistics are compared asymptotic critical values when available a local monte carlo or parametric bootstrap test procedure and a maximized monte carlo mmc procedure the size and power properties of the proposed tests are examined in a simulation experiment the results indicate that the c based tests built upon the simple moment estimator available in closed form have good size and power properties for regular hypotheses while monte carlo tests are much more reliable than those based on asymptotic critical values further in cases where the parametric bootstrap appears to fail for example in the presence of identification problems the mmc procedure easily controls the level of the tests moreover mmc based tests exhibit relatively good power performance despite the conservative feature of the procedure finally we present an application to a time series of returns on the standard and poor s composite price index

generalized spectral testing for multivariate continuous time models we develop an omnibus specification test for multivariate continuous time models using the conditional characteristic function which often has a convenient closed form or can be accurately approximated for many multivariate continuous time models in finance and economics the proposed test fully exploits the information in the joint conditional distribution of underlying economic processes and hence is expected to have good power in a multivariate context a class of easy to interpret diagnostic procedures is supplemented to gauge possible sources of model misspecification our tests are also applicable to discrete time distribution models simulation studies show that the tests provide reliable inference in finite samples

the pricing of credit default swaps under a generalized mixed fractional brownian motion abstract in this paper we consider the pricing of the cds credit default swap under a gmfbm generalized mixed fractional brownian motion model as the name suggests the gmfbm model is indeed a generalization of all the fbm fractional brownian motion models used in the literature and is proved to be able to effectively capture the long range dependence of the stock returns to develop the pricing mechanics of the cds we firstly derive a sufficient condition for the market modeled under the gmfbm to be arbitrage free then under the risk neutral assumption the cds is fairly priced by investigating the two legs of the cash flow involved the price we obtained involves elementary functions only and can be easily implemented for practical purpose finally based on numerical experiments we analyze quantitatively the impacts of different parameters on the prices of the cds interestingly in comparison with all the other fbm models documented in the literature the results produced from the gmfbm model are in a better agreement with those calculated from the classical black scholes model

is the diurnal pattern sufficient to explain intraday variation in volatility a nonparametric assessment abstract in this paper we propose a nonparametric way to test the hypothesis that time variation in intraday volatility is caused solely by a deterministic and recurrent diurnal pattern we assume that noisy high frequency data from a discretely sampled jump diffusion process are available the test is then based on asset returns which are deflated by the seasonal component and therefore homoskedastic under the null to construct our test statistic we extend the concept of pre averaged bipower variation to a general ito semimartingale setting via a truncation device we prove a central limit theorem for this statistic and construct a positive semi definite estimator of the asymptotic covariance matrix the t statistic after pre averaging and jump truncation diverges in the presence of stochastic volatility and has a standard normal distribution otherwise we show that replacing the true diurnal factor with a model free jump and noise robust estimator does not affect the asymptotic theory a monte carlo simulation also shows this substitution has no discernable impact in finite samples the test is however distorted by small infinite activity price jumps to improve inference we propose a new bootstrap approach which leads to almost correctly sized tests of the null hypothesis we apply the developed framework to a large cross section of equity high frequency data and find that the diurnal pattern accounts for a rather significant fraction of intraday variation in volatility but important sources of heteroskedasticity remain present in the data

an improved systolic architecture for 2 d digital filters an improved systolic architecture for two dimensional infinite impulse response iir and finite impulse response fir digital filters is presented comparisons with recently published work are made when compared with the architecture of m a sid ahmed 1989 a substantial reduction in the number of delay elements is observed this reduction is of the order of 10 sup 2 for a 2 d iir filter and equals n 1 for an nth order 2 d fir filter the clock period has been made independent of the order of the filter the speed up factor is the maximum achievable and is independent of the filter order comparison with the work of s sunder et al 1990 shows an improvement in the latency of the systolic array which has been reduced from 1 to 0 a reduction of n 1 delay elements has been achieved for the fir filter an error analysis for the architecture is made

tridiagonal pairs and the μ conjecture let f denote a field and let v denote a vector space over f with finite positive dimension we consider a pair of linear transformations a v v and a v v that satisfy the following conditions i each of a a is diagonalizable ii there exists an ordering vi i 0d of the eigenspaces of a such that a vi vi 1 vi vi 1 for 0 i d where v 1 0 and vd 1 0 iii there exists an ordering vi i 0 of the eigenspaces of a such that avi vi 1 vi vi 1 for 0 i where v 1 0 and v 1 0 iv there is no subspace w of v such that aw w a w w w 0 w v we call such a pair a tridiagonal pair on v it is known that d and for 0 i d the dimensions of vi vd i vi vd i coincide we say the pair a a is sharp whenever dimv0 1 it is known that if f is algebraically closed then a a is sharp a conjectured classification of the sharp tridiagonal pairs was recently introduced by t ito and the second author we present a result which supports the conjecture given scalars i i 0d i i 0d in f that satisfy the known constraints on the eigenvalues of a tridiagonal pair we define an f algebra t by generators and relations we consider the f algebra e0 te0 for a certain idempotent e0 t let f x1 xd denote the polynomial algebra over f involving d mutually commuting indeterminates we display a surjective f algebra homomorphism f x1 xd e0 te0 we conjecture that is an isomorphism we show that this conjecture implies the classification conjecture and that the conjecture holds for d 5

detrended fluctuation analysis on spot and futures markets of west texas intermediate crude oil abstract in this paper we study the auto correlations and cross correlations of west texas intermediate wti crude oil spot and futures return series employing detrended fluctuation analysis dfa and detrended cross correlation analysis dcca scaling analysis shows that for time scales smaller than a month the auto correlations and cross correlations are persistent for time scales larger than a month but smaller than a year the correlations are anti persistent while for time scales larger than a year the series are neither auto correlated nor cross correlated indicating the efficient operation of the crude oil markets moreover for small time scales the degree of short term cross correlations is higher than that of auto correlations using the multifractal extension of dfa and dcca we find that for small time scales the correlations are strongly multifractal while for large time scales the correlations are nearly monofractal analyzing the multifractality of shuffled and surrogated series we find that both long range correlations and fat tail distributions make important contributions to the multifractality our results have important implications for market efficiency and asset pricing models

out of sample forecasts of quadratic variation we compare the forecasts of quadratic variation given by the realized volatility rv and the two scales realized volatility tsrv computed from high frequency data in the presence of market microstructure noise under several different dynamics for the volatility process and assumptions on the noise we show that tsrv largely outperforms rv whether looking at bias variance rmse or out of sample forecasting ability an empirical application to all djia stocks confirms the simulation results

tridiagonal pairs of q racah type abstract let f denote an algebraically closed field and let v denote a vector space over f with finite positive dimension we consider a pair of linear transformations a v v and a v v that satisfy the following conditions i each of a a is diagonalizable ii there exists an ordering v i i 0 d of the eigenspaces of a such that a v i v i 1 v i v i 1 for 0 i d where v 1 0 and v d 1 0 iii there exists an ordering v i i 0 of the eigenspaces of a such that a v i v i 1 v i v i 1 for 0 i where v 1 0 and v 1 0 iv there is no subspace w of v such that a w w a w w w 0 w v we call such a pair a tridiagonal pair on v it is known that d for 0 i d let i resp i denote the eigenvalue of a resp a associated with v i resp v i the pair a a is said to have q racah type whenever i a b q 2 i d c q d 2 i and i a b q 2 i d c q d 2 i for 0 i d where q a b c a b c are scalars in f with q b c b c nonzero and q 2 1 1 this type is the most general one we classify up to isomorphism the tridiagonal pairs over f that have q racah type our proof involves the representation theory of the quantum affine algebra u q sl 2

singular perturbations for boundary value problems arising from exotic options we study the pricing of three exotic derivative securities barrier lookback and passport options which can be characterized by boundary value pde problems in the context of popular markovian sv models of stock prices by extending the fast mean reverting asymptotic analysis in j p fouque g papanicolaou and k r sircar derivatives in financial markets with stochastic volatility cambridge university press london 2000 the usual greek correction to the black scholes prices of these contracts is further corrected by a boundary integral term that is rapidly computed numerically in the case of the passport option the asymptotic method is effective in accounting for sv effects in a simple and robust fashion even in the presence of a highly nonlinear embedded stochastic control problem

estimating stochastic differential equations efficiently by minimum chi squared summary we propose a minimum chi squared estimator for the parameters of an ergodic system of stochastic differential equations with partially observed state we prove that the efficiency of the estimator approaches that of maximum likelihood as the number of moment functions entering the chi squared criterion increases and as the number of past observations entering each moment function increases the minimised criterion is asymptotically chi squared and can be used to test system adequacy when a fitted system is rejected inspecting studentised moments suggests how the fitted system might be modified to improve the fit the method and diagnostic tests are applied to daily observations on the u s dollar to deutschmark exchange rate from 1977 to 1992

alternative models for stock price dynamics abstract this paper evaluates the role of various volatility specifications such as multiple stochastic volatility sv factors and jump components in appropriate modeling of equity return distributions we use estimation technology that facilitates nonnested model comparisons and use a long data set which provides rich information about the conditional and unconditional distribution of returns we consider two broad families of models 1 the multifactor loglinear family and 2 the affine jump family both classes of models have attracted much attention in the derivatives and econometrics literatures there are various tradeoffs in considering such diverse specifications if pure diffusion sv models are chosen over jump diffusions it has important implications for hedging strategies if logarithmic models are chosen over affine ones it may seriously complicate option pricing comparing many different specifications of pure diffusion multifactor models and jump diffusion models we find that 1 log linear models have to be extended to two factors with feedback in the mean reverting factor 2 affine models have to have a jump in returns stochastic volatility or probably both models 1 and 2 are observationally equivalent on the data set in hand in either 1 or 2 the key is that the volatility can move violently as we obtain models with comparable empirical fit one must make a choice based on arguments other than statistical goodness of fit criteria the considerations include facility to price options to hedge and parsimony the affine specification with jumps in volatility might therefore be preferred because of the closed form derivatives prices

estimation of stochastic volatility models with diagnostics abstract efficient method of moments emm is used to fit the standard stochastic volatility model of various extensions to several daily financial time series emm matches to the score of the model determined by data analysis called the score generator discrepancies reveal characteristics of data that stochastic volatility models cannot approximate the two score generators employed here are semiparametric arch and nonlinear nonparametric with the first the standard model is rejected although some extensions are accepted with the second all versions are rejected the extensions required for an adequate fit are so elaborate that nonparametric specifications are probably more convenient

estimating option greeks under the stochastic volatility using simulation abstract as the black scholes bs equation being widely used to price options which is based on a hypothesis that the underlying bonds stocks volatility is constant many scholars proposed the extended version of this formula to predict the behavior of the volatility so stochastic volatility model is the improved version in which fixed volatility is replaced the purpose of this study is to adopt one of the famous stochastic volatility models heston model 1993 to price european call options put option values can easily obtained by call put parity if it is needed simulation has proved to be a valuable tool for estimating options price derivatives i e greeks this paper proposes the method for the simulation of stock prices and variance under the heston stochastic volatility model we consider three different models based on the heston model we present two direct methods a path wise method and likelihood ratio method for estimating the derivatives of options then we compare it with black scholes equation and make a sensitivity analysis for its parameters by using estimator s approaches

default probability of american lookback option in a mixed jump diffusion model abstract this paper considers the default probability of american lookback option in a mixed jump diffusion model where the underlying asset price has to cross two sided predetermined strikes to activate the american lookback option we study a default problem with the bankruptcy time being defined as the first passage time of the underlying asset price by solving a system of coupled mjd fbm we obtain an explicit formula for the laplace transform of the default time some numerical results are given for illustration

long term correlations and multifractal nature in the intertrade durations of a liquid chinese stock and its warrant abstract the intertrade duration of equities is an important financial measure characterizing trading activities it is defined as the waiting time between successive trades of an equity using the ultrahigh frequency data of a liquid chinese stock and its associated warrant we perform a comparative investigation of the statistical properties of their intertrade duration time series the distributions of the two equities can be better described by the shifted power law form than the weibull form and their scaled distributions do not collapse onto a single curve although the intertrade durations of the two equities have very different magnitude their intraday patterns exhibit very similar shapes both detrended fluctuation analysis dfa and detrending moving average analysis dma show that the 1 min intertrade duration time series of the two equities are strongly correlated in addition both multifractal detrended fluctuation analysis mfdfa and multifractal detrending moving average analysis mfdma unveil that the 1 min intertrade durations possess multifractal nature however the difference between the two singularity spectra of the two equities obtained from the mfdma is much smaller than that from the mfdfa

efficient hedging currency options in fractional brownian motion model with jumps abstract this paper deals with the problem of efficient hedging for european currency option and exchange option in case that exchange rate is driven by a fractional brownian motion with jumps in a complete market as long as a seller receives a price of the option equal to the expectation under the risk neutral probability measure of the discounted payoff the seller can hedge this payoff perfectly as the price is often quite expensive the investors need partial hedges which require less capital and reduce the risk the efficient hedge is one of partial hedges the efficient hedging results for options are obtained under fractional brownian motion model with jumps using the equivalent martingale measure simulation results and empirical studies confirm the theoretical findings and show that the fractional brownian motion model with jumps is reasonable

pricing geometric asian power options under mixed fractional brownian motion environment abstract it has been observed that the stock price process can be modeled with driving force as a mixed fractional brownian motion with hurst index h 3 4 whenever long range dependence is possibly present we obtain a closed form expression for the price of a geometric asian option under the mixed fractional brownian motion environment we consider also asian power options when the payoff function is a power function

a discrete time model for daily s p500 returns and realized variations jumps and leverage effects abstract we develop an empirically highly accurate discrete time daily stochastic volatility model that explicitly distinguishes between the jump and continuous time components of price movements using nonparametric realized variation and bipower variation measures constructed from high frequency intraday data the model setup allows us to directly assess the structural inter dependencies among the shocks to returns and the two different volatility components the model estimates suggest that the leverage effect or asymmetry between returns and volatility works primarily through the continuous volatility component the excellent fit of the model makes it an ideal candidate for an easy to implement auxiliary model in the context of indirect estimation of empirically more realistic continuous time jump diffusion and levy driven stochastic volatility models effectively incorporating the interdaily dependencies inherent in the high frequency intraday data

on the functional estimation of jump diffusion models abstract we provide a general asymptotic theory for the fully functional estimates of the infinitesimal moments of continuous time models with discontinuous sample paths of the jump diffusion type minimal requirements are placed on the dynamic properties of the underlying jump diffusion process i e stationarity is not required our theoretical framework justifies consistent in a statistical sense nonparametric extraction of the parameters and functions that drive the dynamic evolution of the process of interest i e the potentially nonaffine and level dependent intensity of the jump arrival being an example from the estimated infinitesimal conditional moments as suggested in johannes 2003 the statistical and economic role of jumps in continuous time interest rate models journal of finance forthcoming

testing for jumps when asset prices are observed with noise a swap variance approach abstract this paper proposes a new test for jumps in asset prices that is motivated by the literature on variance swaps formally the test follows by a direct application of ito s lemma to the semi martingale process of asset prices and derives its power from the impact of jumps on the third and higher order return moments intuitively the test statistic reflects the cumulative gain of a variance swap replication strategy which is known to be minimal in the absence of jumps but substantial in the presence of jumps simulations show that the jump test has nice properties and is generally more powerful than the widely used bi power variation test an important feature of our test is that it can be applied in analytically modified form to noisy high frequency data and still retain power as a by product of our analysis we obtain novel analytical results regarding the impact of noise on bi power variation an empirical illustration using ibm trade data is also included

use and misuse of some hurst parameter estimators applied to stationary and non stationary financial time series abstract the detection of long range dependence lrd is an important task in time series analysis lrd is often summarized by the well known hurst parameter or exponent h 0 1 which can be estimated by a number of methods some of these techniques are designed to be applied to signals behaving as a stationary fractional gaussian noise fgn whereas others imply that the analyzed time series behave as a non stationary fractional brownian motion fbm moreover some estimators do not yield the hurst parameter but indexes related to h and ranging outside the unit interval therefore the fgn or fbm nature of the studied time series has to be preliminarily analyzed before applying any estimation method and the relationships between h and the indexes resulting from the analyses have to be taken into account to obtain coherent results since fgn like series represent the increments of fbm like processes and both the signals are characterized by the same h value by definition estimators designed for fgn like series can be applied to fbm like sequences after preventive differentiation and conversely estimators designed for fbm like processes can be applied to fgn like series after preventive integration the signal characterization is particularly important when h is estimated on financial time series because the returns represent the first difference of price time series which are often assumed to behave like self affine sequences the analysis of simulated fgn and fbm time series shows that all the considered methods yield comparable h values when properly applied the reanalysis of several market price time series already studied in the literature points out that a correct application of the estimators supported by a preventive signal classification yields homogeneous h values allowing for a useful cross validation of results reported in different works moreover some conclusions reported in the literature about the anti persistence of some financial series are shown to be incorrect because of the inappropriate application of the estimation methods

empirical reverse engineering of the pricing kernel abstract this paper proposes an econometric procedure that allows the estimation of the pricing kernel without either any assumptions about the investors preferences or the use of the consumption data we propose a model of equity price dynamics that allows for i simultaneous consideration of multiple stock prices ii analytical formulas for derivatives such as futures options and bonds and iii a realistic description of all of these assets the analytical specification of the model allows us to infer the dynamics of the pricing kernel the model calibrated to a comprehensive dataset including the s p 500 index individual equities t bills and gold futures yields the conditional filter of the unobservable pricing kernel as a result we obtain the estimate of the kernel that is positive almost surely i e precludes arbitrage consistent with the equity risk premium the risk free discounting and with the observed asset prices by construction the pricing kernel estimate involves a highly nonlinear function of the contemporaneous and lagged returns on the s p 500 index this contradicts typical implementations of capm that use a linear function of the market proxy return as the pricing kernel hence the s p 500 index does not have to coincide with the market portfolio if it is used in conjunction with nonlinear asset pricing models we also find that our best estimate of the pricing kernel is not consistent with the standard time separable utilities but potentially could be cast into the stochastic habit formation framework of campbell and cochrane j political economy 107 1999 205

fractional wishart processes and e fractional wishart processes with applications abstract in this paper we introduce two new matrix stochastic processes fractional wishart processes and e fractional wishart processes with integer indices which are based on the fractional brownian motions and then extend e fractional wishart processes to the case with non integer indices both processes include classic wishart processes if the hurst index h equals 1 2 and present serial correlation of stochastic processes applying e fractional wishart processes to financial volatility theory the financial models account for the stochastic volatilities of the assets and for the stochastic correlations not only between the underlying assets returns but also between their volatilities and for stochastic serial correlation of the relevant assets

stock loan valuation based on the finite moment log stable process abstract the empirical test suggests that the log return series of stock price in us market reject the normal distribution and admit instead a subclass of the asymmetric distribution in this paper we investigate the stock loan problem under the assumption that the return of stock follows the finite moment log stable process fmls in this case the pricing model of stock loan can be described by a space fractional partial differential equation with time varying free boundary condition firstly a penalty term is introduced to change the original problem to be defined on a fixed domain and then a fully implicit difference scheme has been developed secondly based on the fully implicit scheme we prove that the stock loan value generated by the penalty method cannot fall below the value obtained when the stock loan is exercised early thirdly the numerical experiments are carried out to demonstrate differences of stock loan model under the fmls and the standard normal distribution optimal redemption strategy of stock loan has been achieved furthermore the impact of key parameters in our model on the stock loan evaluation are analyzed and some reasonable explanation are given