on a higher order secant method in this paper we carry out a modification of the classical secant method our goal is to accelerate the convergence until order two but without using any derivative two convergence theorems are presented finally some numerical experiments are analyzed

a markov model of financial returns abstract we address the general problem of how to quantify the kinematics of time series with stationary first moments but having non stationary multifractal long range correlated second moments we show that a markov process is sufficient to model important aspects of the multifractality observed in financial time series and propose a kinematic model of price fluctuations we test the proposed model by analyzing index closing prices of the new york stock exchange and the dem usd tick by tick exchange rates obtained from reuters efx we show that the model captures the characteristic features observed in actual financial time series including volatility clustering time scaling and fat tails in the probability density functions power law behavior of volatility correlations and most importantly the observed nonuniversal multifractal singularity spectrum motivated by our finding of strong agreement between the model and the data we argue that at least two independent stochastic gaussian variables are required to adequately model price fluctuations

oscillation criteria of yan type for linear hamiltonian systems abstract new oscillation criteria of yan type are established for the linear hamiltonian system x x a t x b t y t t0 y c t x a t y where a t b t and c t are continuous n n matrix valued functions with b t b t 0 c t c t the criteria obtained generalize and improve some previous results for the second order linear matrix differential systems in literature

modeling maxima with autoregressive conditional frechet model abstract this paper introduces a novel dynamic generalized extreme value gev framework for modeling the time varying behavior of maxima in financial time series specifically an autoregressive conditional frechet acf model is proposed in which the maxima are modeled by a frechet distribution with time varying scale parameter volatility and shape parameter tail index conditioned on past information the acf provides a direct and accurate modeling of the time varying behavior of maxima and furthermore offers a new angle to study the tail risk dynamics in financial markets probabilistic properties of acf are studied and a maximum likelihood estimator is used for model estimation with its statistical properties investigated simulations show the flexibility of acf and confirm the reliability of its estimators two real data examples on cross sectional stock returns and high frequency foreign exchange returns are used to demonstrate the acf modeling approach where significant improvement over the static gev has been observed for market tail risk monitoring and conditional var estimation empirical result of acf is consistent with the findings of the dynamic peak over threshold pot literature that the tail index of financial markets varies through time

option pricing stochastic volatility singular dynamics and constrained path integrals abstract stochastic volatility models have been widely studied and used in the financial world the heston model heston 1993 7 is one of the best known models to deal with this issue these stochastic volatility models are characterized by the fact that they explicitly depend on a correlation parameter which relates the two brownian motions that drive the stochastic dynamics associated to the volatility and the underlying asset solutions to the heston model in the context of option pricing using a path integral approach are found in lemmens et al 2008 21 while in baaquie 2007 1997 12 13 propagators for different stochastic volatility models are constructed in all previous cases the propagator is not defined for extreme cases 1 it is therefore necessary to obtain a solution for these extreme cases and also to understand the origin of the divergence of the propagator in this paper we study in detail a general class of stochastic volatility models for extreme values 1 and show that in these two cases the associated classical dynamics corresponds to a system with second class constraints which must be dealt with using dirac s method for constrained systems dirac 1958 1967 22 23 in order to properly obtain the propagator in the form of a euclidean hamiltonian path integral henneaux and teitelboim 1992 25 after integrating over momenta one gets an euclidean lagrangian path integral without constraints which in the case of the heston model corresponds to a path integral of a repulsive radial harmonic oscillator in all the cases studied the price of the underlying asset is completely determined by one of the second class constraints in terms of volatility and plays no active role in the path integral

oscillation results for linear hamiltonian systems for linear hamiltonian systems this paper established some new oscillation criteria which improve previous results even for self adjoint second order differential systems the main tool used is a generalized riccati transformation

a convergence theorem for newton like methods under generalized chen yamamoto type assumptions in this study we provide sufficient conditions for the convergence of a newton like method to a locally unique solution of a nonlinear equation with a nondifferentiable term in a banach space setting we introduce new conditions by assuming the existence of real functions of two variables that serve as upper bounds on the operators involved special choices of the real functions mentioned above lead to chen yamamoto type assumptions or the usual lipschitz conditions associated with the frechet derivatives of the nonlinear operators involved using the majorant method we show that if a certain scalar inequality has a minimum positive solution then the abstract equation has a locally unique solution also we also show that our upper bounds on the distances x n 1 x n and x n x improve on earlier ones found by chen yamamoto dennis rheinboldt and potra et al finally our results can apply to solve nonlinear integral equations of uryson type

modelling price dynamics a hybrid truncated levy flight garch approach abstract arch and garch stochastic processes are widely used in finance and are generally accepted as good approximations when modelling the price dynamics with gaussian conditional probability it can be seen that certain aspects of the empirical data for asset price changes seems to more closely fit a truncated levy flight or garch model but each with individual shortfalls in this paper therefore we combine the garch process with a conditional truncated levy distribution in order to build a hybrid model that most notably describes the price change and associated volatility probability density distributions and scaling behaviour over different time horizons

option pricing formulas based on a non gaussian stock price model options are financial instruments that depend on the underlying stock we explain their non gaussian fluctuations using the nonextensive thermodynamics parameter q a generalized form of the black scholes bs partial differential equation and some closed form solutions are obtained the standard bs equation q 1 which is used by economists to calculate option prices requires multiple values of the stock volatility known as the volatility smile using q 1 5 which well models the empirical distribution of returns we get a good description of option prices using a single volatility

new oscillation criteria for linear matrix hamiltonian systems abstract some new oscillation criteria are established for the matrix linear hamiltonian system x a t x b t y y c t x a t y under the hypothesis a t b t b t 0 and c t c t are n n real continuous matrix functions on the interval t 0 t 0 these results are sharper than some previous results even for self adjoint second order matrix differential systems

on the extremes of a class of non linear processes with heavy tailed innovations the aim of this paper is to look at the limiting form of certain empirical point processes induced by a particular class of non linear processes generated by heavy tailed innovations such asymptotic results will be highly useful in obtaining the weak limiting behavior of various functionals of the underlying process including the asymptotic distribution of upper and lower order statistics in particular we investigate the maximum limiting distribution and its corresponding extremal index the results are applied to the study of the extremal properties of bilinear processes

multifractal model of asset returns with leverage effect abstract multifractal processes are a relatively new tool of stock market analysis their power lies in the ability to take multiple orders of autocorrelations into account explicitly in the first part of the paper we discuss the framework of the lux model and refine the underlying phenomenological picture we also give a procedure of fitting all parameters to empirical data we present a new approach to account for the effective length of power law memory in volatility the second part of the paper deals with the consequences of asymmetry in returns we incorporate two related stylized facts skewness and leverage autocorrelations into the model then from monte carlo measurements we show that this asymmetry significantly increases the mean squared error of volatility forecasts based on a filtering method we give evidence on similar behavior in empirical data

oscillation theorems for self adjoint matrix hamiltonian systems involving general means by use of monotone functionals and positive linear functionals a generalized riccati transformation and the general means technique some new oscillation criteria for the following self adjoint hamiltonian matrix system e x t a t x t b t y t y t c t x t a t y t are obtained the results obtained improve and complement that of kumari et al 2000 on kamenev type theorems moreover these results generalize and improve earlier results due to meng 2002 for e erbe et al 1993 meng et al 1998 and wang 2001 for p t x t q t x t 0 or its special cases and wong 2001 for the scalar system x t q t x t 0

on the invariance of the lagrange multiplier test with respect to certain changes in the alternative hypothesis this paper examines some implications of the observation that the same lagrange multiplier test is sometimes appropriate for quite different alternative hypotheses a characterization of the class of such alternatives is developed which suggests a simple approach to testing for misspecification and the consequences for finite sample power properties are examined by monte carlo experiments

phase distribution and phase correlation of financial time series the scaling phase distribution and phase correlation of financial time series are investigated based on the dow jones industry average and nasdaq 10 min intraday data for a period from 1 aug 1997 to 31 dec 2003 the returns of the two indices are shown to have nice scaling behaviors and belong to stable distributions according to the criterion of l evy s ensuremath alpha stable distribution condition an approach catching characteristic features of financial time series based on the concept of instantaneous phase is further proposed to study the phase distribution and correlation analysis of the phase distribution concludes that return time series fall into a class which is different from other nonstationary time series the correlation between returns of the two indices probed by the distribution of phase difference indicates that there was a remarkable change of trading activities after the event of the 9 11 attack and this change persisted in later trading activities

stochastic volatility models and kelvin waves we use stochastic volatility models to describe the evolution of an asset price its instantaneous volatility and its realized volatility in particular we concentrate on the stein and stein model ssm 1991 for the stochastic asset volatility and the heston model hm 1993 for the stochastic asset variance by construction the volatility is not sign definite in ssm and is non negative in hm it is well known that both models produce closed form expressions for the prices of vanilla option via the lewis lipton formula however the numerical pricing of exotic options by means of the finite difference and monte carlo methods is much more complex for hm than for ssm until now this complexity was considered to be an acceptable price to pay for ensuring that the asset volatility is non negative we argue that having negative stochastic volatility is a psychological rather than financial or mathematical problem and advocate using ssm rather than hm in most applications we extend ssm by adding volatility jumps and obtain a closed form expression for the density of the asset price and its realized volatility we also show that the current method of choice for solving pricing problems with stochastic volatility via the affine ansatz for the fourier transformed density function can be traced back to the kelvin method designed in the 19th century for studying wave motion problems arising in fluid dynamics

value at risk estimation with wavelet based extreme value theory evidence from emerging markets abstract this paper introduces wavelet based extreme value theory evt for univariate value at risk estimation wavelets and evt are combined for volatility forecasting to estimate a hybrid model in the first stage wavelets are used as a threshold in generalized pareto distribution and in the second stage evt is applied with a wavelet based threshold this new model is applied to two major emerging stock markets the istanbul stock exchange ise and the budapest stock exchange bux the relative performance of wavelet based evt is benchmarked against the riskmetrics ewma arma garch generalized pareto distribution and conditional generalized pareto distribution models the empirical results show that the wavelet based extreme value theory increases predictive performance of financial forecasting according to number of violations and tail loss tests the superior forecasting performance of the wavelet based evt model is also consistent with basel ii requirements and this new model can be used by financial institutions as well

new oscillation criteria for linear matrix hamiltonian systems some new criteria have been obtained for the oscillation of the linear matrix hamiltonian system x a t x b t y y c t x a t y under the hypothesis a t b t b t 0 and c t c t are nxn real continuous matrix functions on the interval t 0 t 0 our results are independent of the main results obtained in our recent paper appl math comput 131 2002 357 in the sense that they are given in terms of the positive linear functional on the linear space of nxn matrices with real entries at the same time our results improve some previous results to a great extent which can be seen by the examples given at the end of this paper

the quantum dark side of the optimal control theory abstract in a recent article a generic optimal control problem was studied from a physicist s point of view contreras et al 2017 through this optic the pontryagin equations are equivalent to the hamilton equations of a classical constrained system by quantizing this constrained system using the right ordering of the operators the corresponding quantum dynamics given by the schrodinger equation is equivalent to that given by the hamilton jacobi bellman equation of bellman s theory the conclusion drawn there were based on certain analogies between the equations of motion of both theories in this paper a closer and more detailed examination of the quantization problem is carried out by considering three possible quantization procedures right quantization left quantization and feynman s path integral approach the bellman theory turns out to be the classical limit 0 of these three different quantum theories also the exact relation of the phase s x t of the wave function x t e i s x t of the quantum theory with bellman s cost function j x t is obtained in fact s x t satisfies a conjugate form of the hamilton jacobi bellman equation which implies that the cost functional j x t must necessarily satisfy the usual hamilton jacobi bellman equation thus the bellman theory effectively corresponds to a quantum view of the optimal control problem

trading activity as driven poisson process comparison with empirical data we propose the point process model as the poissonian like stochastic sequence with slowly diffusing mean rate and adjust the parameters of the model to the empirical data of trading activity for 26 stocks traded on nyse the proposed scaled stochastic differential equation provides the universal description of the trading activities with the same parameters applicable for all stocks

leverage effect in financial markets the retarded volatility model we investigate quantitatively the so called leverage effect which corresponds to a negative correlation between past returns and future volatility for individual stocks this correlation is moderate and decays over 50 days while for stock indices it is much stronger but decays faster for individual stocks the magnitude of this correlation has a universal value that can be rationalized in terms of a new retarded model which interpolates between a purely additive and a purely multiplicative stochastic process for stock indices a specific amplification phenomenon seems to be necessary to account for the observed amplitude of the effect

a top bottom price approach to understanding financial fluctuations abstract the presence of sequences of top and bottom tb events in financial series is investigated for the purpose of characterizing such switching points they clearly mark a change in the trend of rising or falling prices of assets to the opposite tendency are of crucial importance for the players decision and also for the market stability previous attempts to characterize switching points have been based on the behavior of the volatility and on the definition of microtrends the approach used herein is based on the smoothing of the original data with a gaussian kernel the events are identified by the magnitude of the difference of the extreme prices by the time lag between the corresponding events waiting time and by the time interval between events with a minimal magnitude return time results from the analysis of the inter day dow jones industrial average index djia from 1928 to 2011 are discussed q gaussian functions with power law tails are found to provide a very accurate description of a class of measures obtained from the series statistics

impact of foreign exchange rate on oil companies risk in stock market during the recent years the importance of effective risk management has become extremely crucial value at risk var is a standard downside measure to explain the behavior of financial series as the garch models have been successfully applied in modeling the volatility structure of securities and other financial assets the var of garch models has turned into an important quantity to study in addition to garch family models the markov regime switching garch mrs garch models are a widely used approach to model financial volatility with potential structural breaks in this paper we evaluated the performance of the mrs garch models with the traditional arma garch family models for estimating var of the stock return of operating companies in the oil industry srocoi in irans stock market under the normal student t and ged distributions our findings showed that the mrs garch models outperform the arma garch family models to capture the characteristics of the srocois volatility additionally we evaluated impact of the foreign exchange rate fluctuations on the var of srocois that were calculated from the optimal models under two regimes usingardl model the results further demonstrated that foreign exchange rate fluctuations have significant and different impacts on the var of srocois across regimes we modeled srocois in irans stock market using mrs garch and arma garch family models mrs garch models under student t and ged distributions have better performance to capture srocois we estimated in sample and out of sample var of srocois from optima models we evaluated impact of the foreign exchange rate fluctuations on the var of srocois foreign exchange rate significantly effect on the var of srocois in different regimes

an empirical model of volatility of returns and option pricing abstract this paper reports several entirely new results on financial market dynamics and option pricing we observe that empirical distributions of returns are much better approximated by an exponential distribution than by a gaussian this exponential distribution of asset prices can be used to develop a new pricing model for options in closed algebraic form that is shown to provide valuations that agree very well with those used by traders we show how the fokker planck formulation of fluctuations can be used with a local volatility diffusion coefficient to generate an exponential distribution for asset returns and also how fat tails for extreme returns are generated dynamically by a simple generalization of our new volatility model nonuniqueness in deducing dynamics from empirical data is discussed and is shown to have no practical effect over time scales much less than one hundred years we derive an option pricing pde and explain why it is superfluous because all information required to price options in agreement with the delta hedge is already included in the green function of the fokker planck equation for a special choice of parameters finally we also show how to calculate put and call prices for a stretched exponential returns density

multi asset black scholes model as a variable second class constrained dynamical system abstract in this paper we study the multi asset black scholes model from a structural point of view for this we interpret the multi asset black scholes equation as a multidimensional schrodinger one particle equation the analysis of the classical hamiltonian and lagrangian mechanics associated with this quantum model implies that in this system the canonical momentums cannot always be written in terms of the velocities this feature is a typical characteristic of the constrained system that appears in the high energy physics to study this model in the proper form one must apply dirac s method for constrained systems the results of the dirac s analysis indicate that in the correlation parameters space of the multi assets model there exists a surface called the kummer surface k where the determinant of the correlation matrix is null on which the constraint number can vary we study in detail the cases with n 2 and n 3 assets for these cases we calculate the propagator of the multi asset black scholes equation and show that inside the kummer k surface the propagator is well defined but outside k the propagator diverges and the option price is not well defined on k the propagator is obtained as a constrained path integral and their form depends on which region of the kummer surface the correlation parameters lie thus the multi asset black scholes model is an example of a variable constrained dynamical system and it is a new and beautiful property that had not been previously observed

oscillation criteria for linear matrix hamiltonian systems abstract in this paper we present oscillation criteria in terms of the coefficient functions for the matrix linear hamiltonian system u a x u b x v v c x u a x v under the hypothesis h a x b x b x 0 and c x c x are n n matrices of real valued continuous functions on the interval i a a these criteria generalize earlier results due to etgen and pawlowski 1976 erbe qingkai kong and shigui ruan 1993 and fanwei meng jizhong wang and zhaowen zheng 1998 for the system p x u q x u 0 or its special cases

on the convergence of a certain class of iterative procedures under relaxed conditions with applications we provide sufficient convergence conditions for a certain class of inexact newton like methods to a locally unique solution of a nonlinear equation in a banach space the equation contains a nondifferentiable term and at each step we use the inverse of the same linear operator we use ptak like conditions that are weaker than earlier ones our results apply whenever earlier ones do but not vice versa a semilocal convergence result is also given based on the contraction mapping principle finally our results apply to solve a nonlinear integral equation of uryson type appearing in elasticity theory that cannot be solved with existing methods

on the convergence of two step methods generated by point to point operators in this study we examine conditions for the convergence of two step methods generated by point to point operators iterations of this type have a great importance in optimization theory stability analysis of dynamic systems and many other fields of applied mathematics the speed of convergence is also examined using the theory of majorants in a banach space setting the monotone convergence of these methods is also examined in a partially ordered topological space special cases of our results reduce to corresponding results already in the literature in particular relevant work can be found in i k argyros appl math comput 61 1 1994 51 69 and f szidarovasky and o palusinski appl math comput 64 1994 115 119 and references therein some applications are also given to the solution of systems of nonlinear integral equations of uryson type

weighted means and oscillation conditions for second order matrix differential equations on considere le systeme d equations differentielles d ordre 2 p t y t q t y t 0 pour t 0 ou p et q sont des matrices symetriques n n reelles sur 0 et y un vecteur colonne on suppose que p t est definie positive pour tout t tel que p t 1 on donne des conditions d oscillations

interval oscillation criteria for matrix differential systems with damping abstract this paper concerns the oscillation of solutions to leighton type for the matrix differential system with damping p t y r t y q t y 0 under the hypothesis p t p t 0 q t q t and r t r t are n n matrices of real valued continuous functions on the interval t 0

tests of the random walk hypothesis for financial data abstract we propose a method from the viewpoint of deterministic dynamical systems to investigate whether observed data follow a random walk rw and apply the method to several financial data our method is based on the previously proposed small shuffle surrogate method hence our method does not depend on the specific data distribution although previously proposed methods depend on properties of the data distribution the data we use are stock market standard poor s 500 in us market and nikkei225 in japanese market exchange rate british pound us dollar and japanese yen us dollar and commodity market gold price and crude oil price we found that these financial data are rw whose first differences are independently distributed random variables or time varying random variables

oscillation results for matrix differential systems with damping abstract in this paper we establish several new oscillation theorems of leighton type for the matrix differential system with damping p t y r t y q t y 0 under the hypothesis p t p t 0 q t q t and r t r t are n n matrices of real valued continuous functions on the interval t 0 our results are not contained in known results

path integral approach to asian options in the black scholes model abstract we derive a closed form solution for the price of an average strike as well as an average price geometric asian option by making use of the path integral formulation our results are compared to a numerical monte carlo simulation we also develop a pricing formula for an asian option with a barrier on a control process combining the method of images with a partitioning of the set of paths according to the average along the path this formula is exact when the correlation is zero and is approximate when the correlation increases

path integral approach to closed form option pricing formulas with applications to stochastic volatility and interest rate models we present a path integral method to derive closed form solutions for option prices in a stochastic volatility model the method is explained in detail for the pricing of a plain vanilla option the flexibility of our approach is demonstrated by extending the realm of closed form option price formulas to the case where both the volatility and interest rates are stochastic this flexibility is promising for the treatment of exotic options our analytical formulas are tested with numerical monte carlo simulations

oscillation results for selfadjoint differential systems abstract we consider the second order differential system 1 r t y q t y 0 where r q y are n n matrices with r t q t symmetric and r t positive definite for t a r t 0 t a we establish sufficient conditions in order that all prepared solutions y t of 1 are oscillatory that is det y t vanishes infinitely often on a the conditions involve the smallest and largest eigen values n r 1 t and 1 a t q s ds respectively the results obtained can be regarded as generalizing well known results of leighton and others in the scalar case

random diffusion and leverage effect in financial markets we prove that brownian market models with random diffusion coefficients provide an exact measure of the leverage effect j p bouchaud et al phys rev lett 87 228701 2001 this empirical fact asserts that past returns are anticorrelated with future diffusion coefficient several models with random diffusion have been suggested but without a quantitative study of the leverage effect our analysis lets us to fully estimate all parameters involved and allows a deeper study of correlated random diffusion models that may have practical implications for many aspects of financial markets

model for non gaussian intraday stock returns stock prices are known to exhibit non gaussian dynamics and there is much interest in understanding the origin of this behavior here we present a model that explains the shape and scaling of the distribution of intraday stock price fluctuations called intraday returns and verify the model using a large database for several stocks traded on the london stock exchange we provide evidence that the return distribution for these stocks is non gaussian and similar in shape and that the distribution appears stable over intraday time scales we explain these results by assuming the volatility of returns is constant intraday but varies over longer periods such that its inverse square follows a gamma distribution this produces returns that are student distributed for intraday time scales the predicted results show excellent agreement with the data for all stocks in our study and over all regions of the return distribution

hamiltonian and potentials in derivative pricing models exact results and lattice simulations the pricing of options warrants and other derivative securities is one of the great success of financial economics these financial products can be modeled and simulated using quantum mechanical instruments based on a hamiltonian formulation we show here some applications of these methods for various potentials which we have simulated via lattice langevin and monte carlo algorithms to the pricing of options we focus on barrier or path dependent options showing in some detail the computational strategies involved

a comparison between several correlated stochastic volatility models abstract we compare the most common stochastic volatility models such as the ornstein uhlenbeck ou the heston and the exponential ou models we try to decide which is the most appropriate one by studying their volatility autocorrelation and leverage effect and thus outline the limitations of each model we add empirical research on market indices confirming the universality of the leverage and volatility correlations

volatility a hidden markov process in financial time series volatility characterizes the amplitude of price return fluctuations it is a central magnitude in finance closely related to the risk of holding a certain asset despite its popularity on trading floors volatility is unobservable and only the price is known diffusion theory has many common points with the research on volatility the key of the analogy being that volatility is a time dependent diffusion coefficient of the random walk for the price return we present a formal procedure to extract volatility from price data by assuming that it is described by a hidden markov process which together with the price forms a two dimensional diffusion process we derive a maximum likelihood estimate of the volatility path valid for a wide class of two dimensional diffusion processes the choice of the exponential ornstein uhlenbeck expou stochastic volatility model performs remarkably well in inferring the hidden state of volatility the formalism is applied to the dow jones index the main results are that i the distribution of estimated volatility is lognormal which is consistent with the expou model ii the estimated volatility is related to trading volume by a power law of the form sigma proportional variant v0 55 and iii future returns are proportional to the current volatility which suggests some degree of predictability for the size of future returns

levy walks and enhanced diffusion in milan stock exchange abstract we perform statistical analyses of the general and sectorial historical m i b indices of the milan stock exchange our analyses show that the price indices have statistical properties which are compatible with a levy random walk the time evolution of the daily variations of indices is intermittent on a time scale of years and the variance of almost all indices displays a superdiffusive behavior by using the theory of enhanced diffusion in levy walks as theoretical framework we ascribe the superdiffusive behavior to a nonlocal memory coupling price and time

interval estimation of value at risk based on garch models with heavy tailed innovations arch and garch models are widely used to model financial market volatilities in risk management applications considering a garch model with heavy tailed innovations we characterize the limiting distribution of an estimator of the conditional value at risk var which corresponds to the extremal quantile of the conditional distribution of the garch process we propose two methods the normal approximation method and the data tilting method for constructing confidence intervals for the conditional var estimator and assess their accuracies by simulation studies finally we apply the proposed approach to an energy market data set

a modification of newton s method for nondifferentiable equations in this paper we study the problem of approximating a solution of a nonlinear equation where the operator involved is nondifferentiable having the newton method as origin we construct a uniparametric family of iterative processes to approximate a solution of the equation to finish we consider several test problems

adaptive estimation in time series models in a framework particularly suited for many time series models we obtain a lan result under quite natural and economical conditions this enables us to construct adaptive estimators for part of the euclidean parameter in these semiparametric models special attention is directed to group models in time series with the important subclass of models with time varying location and scale our set up is confronted with the existing literature and as examples we reconsider linear regression and arma tar and arch models

forecasting volatility of fuel oil futures in china garch type sv or realized volatility models abstract in most previous works on forecasting oil market volatility squared daily returns were taken as the proxy of unobserved actual volatility however as demonstrated by andersen and bollerslev 1998 22 this proxy with too high measurement noise could be perfectly outperformed by a so called realized volatility rv measure calculated by the cumulative sum of squared intraday returns with this motivation we further extend earlier works by employing intraday high frequency data to compare the performance of three typical volatility models in the daily out of sample volatility forecasting of fuel oil futures on the shanghai futures exchange shfe the garch type stochastic volatility sv and realized volatility models by taking rv as the proxy of actual daily volatility and then computing forecasting errors we find that the realized volatility model based on intraday high frequency data produces significantly more accurate volatility forecasts than the garch type and sv models based on daily returns furthermore the sv model outperforms many linear and nonlinear garch type models that capture long memory volatility and or the asymmetric leverage effect in volatility these results also prove that abundant volatility information is available in intraday high frequency data and can be used to construct more accurate oil volatility forecasting models

managing distribution changes in time series prediction when a problem is modeled statistically a single distribution model is usually postulated that is assumed to be valid for the entire space nonetheless this practice may be somewhat unrealistic in certain application areas in which the conditions of the process that generates the data may change as far as we are aware however no techniques have been developed to tackle this problem this article proposes a technique for modeling and predicting this change in time series with a view to improving estimates and predictions the technique is applied among other models to the hypernormal distribution recently proposed when tested on real data from a range of stock market indices the technique produces better results that when a single distribution model is assumed to be valid for the entire period of time studied moreover when a global model is postulated it is highly recommended to select the hypernormal distribution parameter in the same likelihood maximization process

maximum entropy autoregressive conditional heteroskedasticity model abstract in many applications it has been found that the autoregressive conditional heteroskedasticity arch model under the conditional normal or student s t distributions are not general enough to account for the excess kurtosis in the data moreover asymmetry in the financial data is rarely modeled in a systematic way in this paper we suggest a general density function based on the maximum entropy me approach that takes account of asymmetry excess kurtosis and also of high peakedness the me principle is based on the efficient use of available information and as is well known many of the standard family of distributions can be derived from the me approach we demonstrate how we can extract information functional from the data in the form of moment functions we also propose a test procedure for selecting appropriate moment functions our procedure is illustrated with an application to the nyse stock returns the empirical results reveal that the me approach with a fewer moment functions leads to a model that captures the stylized facts quite effectively

convergence rates for inexact newton like methods at singular points and applications newton s method converges linearly rather than quadratically if the initial guess is close to the solution and the frechet derivative is singular at the solution several authors have already tried to improve the rate of convergence for this method in this case the limitations of their approach is twofold first the residuals at each step are assumed to be zero which is not the case in general second the previous works are limited only to the ordinary newton method here we extend and improve on these results by providing convergence rates for inexact newton like methods on a banach space setting moreover our results reduce to the ones already in the literature for special choices of the operators involved we complete our study with some numerical examples appearing in connection with some predator prey problems appearing in population modeling that show how our results improve on the earlier ones

multiple time scales and the empirical models for stochastic volatility abstract the most common stochastic volatility models such as the ornstein uhlenbeck ou the heston the exponential ou expou and hull white models define volatility as a markovian process in this work we check the applicability of the markovian approximation at separate times scales and will try to answer the question which of the stochastic volatility models indicated above is the most realistic to this end we consider the volatility at both short a few days and long a few months time scales as a markovian process and estimate for it the coefficients of the kramers moyal expansion using the data for dow jones index it has been found that the empirical data allow to take only the first two coefficients of expansion to be non zero that define form of the volatility stochastic differential equation of ito it proved to be that for the long time scale the empirical data support the expou model at the short time scale the empirical model coincides with expou model for the small volatility quantities only

time evolution of stochastic processes with correlations in the variance stability in power law tails of distributions abstract we model the time series of the s p500 index by a combined process the ar garch process where ar denotes the autoregressive process which we use to account for the short range correlations in the index changes and garch denotes the generalized autoregressive conditional heteroskedastic process which takes into account the long range correlations in the variance we study the ar garch process with an initial distribution of truncated levy form we find that this process generates a new probability distribution with a crossover from a levy stable power law to a power law with an exponent outside the levy range beyond the truncation cutoff we analyze the sum of n variables of the ar garch process and find that due to the correlations the ar garch process generates a probability distribution which exhibits stable behavior in the tails for a broad range of values n a feature which is observed in the probability distribution of the s p500 index we find that this power law stability depends on the characteristic scale in the correlations we also find that inclusion of short range correlations through the ar process is needed to obtain convergence to a limiting gaussian distribution for large n as observed in the data

a newton kantorvich theorem for equations involving m frechet differentiable operators and applications in radiative transfer abstract in this study we approximate a locally unique solution of a nonlinear operator equation in banach space using newton s method a complete error analysis showing the quadratic convergence of our method is also given our new theorem uses lipschitz or holder continuity assumptions on m frechet differentiable operators where m 2 is a positive integer a numerical example is given to show that our results provide a better information on the location of the solution as well as finer error bounds on the distances involved than earlier results a second numerical example shows how to solve a nonlinear integral equation appearing in radiative transfer

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

generalized autoregressive conditional heteroskedasticity a natural generalization of the arch autoregressive conditional heteroskedastic process introduced in engle 1982 to allow for past conditional variances in the current conditional variance equation is proposed stationarity conditions and autocorrelation structure for this new class of parametric models are derived maximum likelihood estimation and testing are also considered finally an empirical example relating to the uncertainty of the inflation rate is presented

a contribution to the systematics of stochastic volatility models abstract we systematically compare several classes of stochastic volatility models of stock market fluctuations we show that the long time return distribution is either gaussian or develops a power law tail while the short time return distribution has generically a stretched exponential form but can also assume an algebraic decay in the family of models which we call garch type the intermediate regime is found in the exponential ornstein uhlenbeck process we also calculate the decay of the autocorrelation function of volatility

forecasting volatility of ssec in chinese stock market using multifractal analysis abstract in this paper taking about 7 years high frequency data of the shanghai stock exchange composite index ssec as an example we propose a daily volatility measure based on the multifractal spectrum of the high frequency price variability within a trading day an arfima model is used to depict the dynamics of this multifractal volatility mfv measures the one day ahead volatility forecasting performances of the mfv model and some other existing volatility models such as the realized volatility model stochastic volatility model and garch are evaluated by the superior prediction ability spa test the empirical results show that under several loss functions the mfv model obtains the best forecasting accuracy

minimal model of financial stylized facts in this work we propose a statistical characterization of a linear stochastic volatility model featuring inverse gamma stationary distribution for the instantaneous volatility we detail the derivation of the moments of the return distribution revealing the role of the inverse gamma law in the emergence of fat tails and of the relevant correlation functions we also propose a systematic methodology for estimating the parameters and we describe the empirical analysis of the standard poor s 500 index daily returns confirming the ability of the model to capture many of the established stylized facts as well as the scaling properties of empirical distributions over different time horizons

estimating semiparametric arch models by kernel smoothing methods we investigate a class of semiparametric arch models that includes as a special case the partially nonparametric pnp model introduced by engle and ng 1993 and which allows for both flexible dynamics and flexible function form with regard to the news impact function we show that the functional part of the model satisfies a type ii linear integral equation and give simple conditions under which there is a unique solution we propose an estimation method that is based on kernel smoothing and profiled likelihood we establish the distribution theory of the parametric components and the pointwise distribution of the nonparametric component of the model we also discuss efficiency of both the parametric part and the nonparametric part we investigate the performance of our procedures on simulated data and on a sample of s p500 index returns we find evidence of asymmetric news impact functions consistent with the parametric analysis

riccati techniques and variational principles in oscillation theory for linear systems on etablit des conditions suffisantes pour que toutes les solutions soient oscillatoires on utilise les techniques de riccati et les principes variationnels

on newton s method under mild differentiability conditions and applications in this study we are concerned with the problem of approximating a locally unique solution of a nonlinear operator equation in a banach space we examine the convergence of the newton kantorovich method by assuming that the frechet derivative of the nonlinear operator involved is only holder continuous many results exist already in the literature to cover the stronger case when the operator is lipschitz continuous moreover we use this study to counter some claims made by galperin and waksman on related work of ours furthermore we use our results to solve a two point boundary value problem appearing in kinetic theory of gasses elasticity and other applied areas

oscillation of two dimensional linear second order differential systems abstract this article is concerned with the oscillatory behavior at infinity of the solution y a r 2 of a system of two second order differential equations y t q t y t 0 t a q is a continuous matrix valued function on a whose values are real symmetric matrices of order 2 it is shown that the solution is oscillatory at infinity if the largest eigenvalue of the matrix at q s ds tends to infinity as t this proves a conjecture of d hinton and r t lewis rocky mountain j math 10 1980 751 766 for the two dimensional case furthermore it is shown that considerably weaker forms of the condition still suffice for oscillatory behavior at infinity

nonextensive statistical mechanics and economics abstract ergodicity this is to say dynamics whose time averages coincide with ensemble averages naturally leads to boltzmann gibbs bg statistical mechanics hence to standard thermodynamics this formalism has been at the basis of an enormous success in describing among others the particular stationary state corresponding to thermal equilibrium there are however vast classes of complex systems which accommodate quite badly or even not at all within the bg formalism such dynamical systems exhibit in one way or another nonergodic aspects in order to be able to theoretically study at least some of these systems a formalism was proposed 14 years ago which is sometimes referred to as nonextensive statistical mechanics we briefly introduce this formalism its foundations and applications furthermore we provide some bridging to important economical phenomena such as option pricing return and volume distributions observed in the financial markets and the fascinating and ubiquitous concept of risk aversion one may summarize the whole approach by saying that bg statistical mechanics is based on the entropy s bg k i p i ln p i and typically provides exponential laws for describing stationary states and basic time dependent phenomena while nonextensive statistical mechanics is instead based on the entropic form s q k 1 i p i q q 1 with s 1 s bg and typically provides for the same type of description asymptotic power laws

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

on the convergence of generalized newton methods and implicit functions abstract in this article we provide sufficient conditions for the convergence of generalized newton methods the linear operators involved are obtained recursively from the previous ones

stochastic volatility models at ρ 1 as second class constrained hamiltonian systems abstract the stochastic volatility models used in the financial world are characterized in the continuous time case by a set of two coupled stochastic differential equations for the underlying asset price s and volatility in addition the correlations of the two brownian movements that drive the stochastic dynamics are measured by the correlation parameter 1 1 this stochastic system is equivalent to the fokker planck equation for the transition probability density of the random variables s and solutions for the transition probability density of the heston stochastic volatility model heston 1993 were explored in dragulescu and yakovenko 2002 where the fundamental quantities such as the transition density itself depend on in such a manner that these are divergent for the extreme limit 1 the same divergent behavior appears in hagan et al 2002 where the probability density of the sabr model was analyzed in an option pricing context the propagator of the bi dimensional black scholes equation was obtained in lemmens et al 2008 in terms of the path integrals and in this case the propagator diverges again for the extreme values 1 this paper shows that these similar divergent behaviors are due to a universal property of the stochastic volatility models in the continuum all of them are second class constrained systems for the most extreme correlated limit 1 in this way the stochastic dynamics of the 1 cases are different of the 1 1 case and it cannot be obtained as a continuous limit from the 1 regimen this conclusion is achieved by considering the fokker planck equation or the bi dimensional black scholes equation as a euclidean quantum schrodinger equation then the analysis of the underlying classical mechanics of the quantum model implies that stochastic volatility models at 1 correspond to a constrained system to study the dynamics in an appropriate form dirac s method for constrained systems dirac 1958 1967 must be employed and dirac s analysis reveals that the constraints are second class in order to obtain the transition probability density or the option price correctly one must evaluate the propagator as a constrained hamiltonian path integral henneaux and teitelboim 1992 in a similar way to the high energy gauge theory models in fact for all stochastic volatility models after integrating over momentum variables one obtains an effective euclidean lagrangian path integral over the volatility alone the role of the second class constraints is determining the underlying asset price s completely in terms of volatility so it plays no role in the path integral in order to examine the effect of the constraints on the dynamics for both extreme limits the probability density function is evaluated by using semi classical arguments in an analogous manner to that developed in hagan et al 2002 for the sabr model

oscillation criteria for second order linear matrix differential systems with damping using a generalization of sturm s comparison theorem some new oscillation criteria are established for the matrix differential system with damping p t y r t y q t y 0 under the hypothesis p t p t 0 q t q t y t are nxn matrices of real valued continuous functions on the interval t 0 and r t r t c 1 t 0 r n 2 our results are sharper than some previous results

dynamic optimization and its relation to classical and quantum constrained systems abstract we study the structure of a simple dynamic optimization problem consisting of one state and one control variable from a physicist s point of view by using an analogy to a physical model we study this system in the classical and quantum frameworks classically the dynamic optimization problem is equivalent to a classical mechanics constrained system so we must use the dirac method to analyze it in a correct way we find that there are two second class constraints in the model one fix the momenta associated with the control variables and the other is a reminder of the optimal control law the dynamic evolution of this constrained system is given by the dirac s bracket of the canonical variables with the hamiltonian this dynamic results to be identical to the unconstrained one given by the pontryagin equations which are the correct classical equations of motion for our physical optimization problem in the same pontryagin scheme by imposing a closed loop strategy the optimality condition for the action gives a consistency relation which is associated to the hamilton jacobi bellman equation of the dynamic programming method a similar result is achieved by quantizing the classical model by setting the wave function x t e i s x t in the quantum schrodinger equation a non linear partial equation is obtained for the s function for the right hand side quantization this is the hamilton jacobi bellman equation when s x t is identified with the optimal value function thus the hamilton jacobi bellman equation in bellman s maximum principle can be interpreted as the quantum approach of the optimization problem

a quantum model of option pricing when black scholes meets schrodinger and its semi classical limit abstract the black scholes equation can be interpreted from the point of view of quantum mechanics as the imaginary time schrodinger equation of a free particle when deviations of this state of equilibrium are considered as a product of some market imperfection such as transaction cost asymmetric information issues short term volatility extreme discontinuities or serial correlations the classical non arbitrage assumption of the black scholes model is violated implying a non risk free portfolio from haven 2002 1 we know that an arbitrage environment is a necessary condition to embedding the black scholes option pricing model in a more general quantum physics setting the aim of this paper is to propose a new black scholes schrodinger model based on the endogenous arbitrage option pricing formulation introduced by contreras et al 2010 2 hence we derive a more general quantum model of option pricing that incorporates arbitrage as an external time dependent force which has an associated potential related to the random dynamic of the underlying asset price this new resultant model can be interpreted as a schrodinger equation in imaginary time for a particle of mass 1 2 with a wave function in an external field force generated by the arbitrage potential as pointed out above this new model can be seen as a more general formulation where the perfect market equilibrium state postulated by the black scholes model represent a particular case finally since the schrodinger equation is in place we can apply semiclassical methods of common use in theoretical physics to find an approximate analytical solution of the black scholes equation in the presence of market imperfections as it is the case of an arbitrage bubble here as a numerical illustration of the potential of this schrodinger equation analogy the semiclassical approximation is performed for different arbitrage bubble forms step linear and parabolic and compare with the exact solution of our general quantum model of option pricing

a convergence theorem for newton like methods in banach spaces on the basis of the results obtained in a series of papers 25 28 a convergence theorem for newton s method in banach spaces is given which improves the theorems of kantorovich 4 lancaster 8 and ostrowski 10 the error bounds obtained improve the recent results of potra 17

oscillation theorems for linear matrix hamiltonian systems using a matrix linear transformation which preserves oscillatory property some new oscillation criteria for the following linear matrix hamiltonian system u a t t i u b t v v c t u t i a t v t t 0 are obtained which improve and generalize some recent results in literature

oscillation of linear hamiltonian systems abstract in this paper sufficient conditions have been obtained for the oscillation of a class of linear hamiltonian systems

a uniparametric family of iterative processes for solving nondifferentiable equations in this work we study a class of secant like iterations for solving nonlinear equations in banach spaces we consider a condition for divided differences which generalizes the usual ones i e lipschitz and holder continuous conditions a semilocal convergence result is obtained for nondifferentiable operators for that we use a technique based on a new system of recurrence relations to obtain domains of existence and uniqueness of the solution finally we apply our results to the numerical solution of several examples

riccati techniques and oscillation for self adjoint matrix hamiltonian systems the purpose of this paper is to develop a generalized matrix riccati technique for the self adjoint matrix hamiltonian system u a x u b x v v c x u a x v together with the integral averaging technique and monotone functionals new oscillation and interval oscillation criteria are established for the system these criteria extend improve complement a number of existing results and handle some cases not covered by known criteria in particular two interesting examples are included to illustrate the versatility of our results

testing forecast optimality under unknown loss empirical tests of forecast optimality have traditionally been conducted under the assumption of mean squared error loss or some other known loss function in this article we establish new testable properties that hold when the forecaster s loss function is unknown but testable restrictions can be imposed on the data generating process trading off conditions on the data generating process against conditions on the loss function we propose flexible estimation of the forecaster s loss function in situations where the loss depends not only on the forecast error but also on other state variables such as the level of the target variable we apply our results to the problem of evaluating the federal reserve s forecasts of output growth forecast optimality is rejected if the fed s loss depends only on the forecast error however the empirical findings are consistent with forecast optimality provided that overpredictions of output growth are costlier to the fed than underpredictions particularly during per