jump tails extreme dependencies and the distribution of stock returns we provide a new framework for estimating the systematic and idiosyncratic jump tail risks in financial asset prices our estimates are based on in fill asymptotics for directly identifying the jumps together with extreme value theory evt approximations and methods of moments for assessing the tail decay parameters and tail dependencies on implementing the procedures with a panel of intraday prices for a large cross section of individual stocks and the s p 500 market portfolio we find that the distributions of the systematic and idiosyncratic jumps are both generally heavy tailed and close to symmetric and show how the jump tail dependencies deduced from the high frequency data together with the day to day variation in the diffusive volatility account for the extreme joint dependencies observed at the daily level

variation and efficiency of high frequency betas abstract this paper studies the efficient estimation of betas from high frequency return data on a fixed time interval under an assumption of equal diffusive and jump betas we derive the semiparametric efficiency bound for estimating the common beta and develop an adaptive estimator that attains the efficiency bound we further propose a hausman type test for deciding whether the common beta assumption is true from the high frequency data in our empirical analysis we provide examples of stocks and time periods for which a common market beta assumption appears true and ones for which this is not the case we further quantify empirically the gains from the efficient common beta estimation developed in the paper

nonparametric inference on levy measures and copulas in this paper nonparametric methods to assess the multivariate levy measure are introduced starting from high frequency observations of a levy process x we construct estimators for its tail integrals and the pareto levy copula and prove weak convergence of these estimators in certain function spaces given n observations of increments over intervals of length n the rate of convergence is k 1 2 n for kn n n which is natural concerning inference on the levy measure analytic properties of the pareto levy copula which to the best of our knowledge have not been mentioned before in the literature are provided as well we conclude with a short simulation study on the performance of our estimators

a method for calculating bounds on the asymptotic covariance matrices of generalized method of moments estimators abstract for many time series estimation problems there is an infinite dimensional class of generalized method of moments estimators that are consistent and asymptotically normal this paper suggests a procedure for calculating the greatest lower bound for the asymptotic covariance matrices of such estimators the analysis focuses on estimation problems in which the data are generated by a stochastic process that is stationary and ergodic the calculation of the bound uses martingale difference approximations as suggested by gordon 1969 and a matrix version of hilbert space methods

time varying periodicity in intraday volatility abstractwe develop a nonparametric test for whether return volatility exhibits time varying intraday periodicity using a long time series of high frequency data our null hypothesis commonly adopt

inverse realized laplace transforms for nonparametric volatility density estimation in jump diffusions this article develops a nonparametric estimator of the stochastic volatility density of a discretely observed ito semimartingale in the setting of an increasing time span and finer mesh of the observation grid there are two basic steps involved the first step is aggregating the high frequency increments into the realized laplace transform which is a robust nonparametric estimate of the underlying volatility laplace transform the second step is using a regularized kernel to invert the realized laplace transform these two steps are relatively quick and easy to compute so the nonparametric estimator is practicable the article also derives bounds for the mean squared error of the estimator the regularity conditions are sufficiently general to cover empirically important cases such as level jumps and possible dependencies between volatility moves and either diffusive or jump moves in the semimartingale the monte carlo analysis in this study indicates that the nonparametric estimator is reliable and re

time varying jump tails we develop new methods for the estimation of time varying risk neutral jump tails in asset returns in contrast to existing procedures based on tightly parameterized models our approach imposes much fewer structural assumptions relying on extreme value theory approximations together with short maturity options the new estimation approach explicitly allows the parameters characterizing the shape of the right and the left tails to differ and importantly for the tail shape parameters to change over time on implementing the procedures with a panel of s p 500 options our estimates clearly suggest the existence of highly statistically significant temporal variation in both of the tails we further relate this temporal variation in the shape and the magnitude of the jump tails to the underlying return variation through the formulation of simple time series models for the tail parameters

the distribution of realized exchange rate volatility using high frequency data on deutschemark and yen returns against the dollar we construct model free estimates of daily exchange rate volatility and correlation that cover an entire decade our estimates termed realized volatilities and correlations are not only model free but also approximately free of measurement error under general conditions which we discuss in detail hence for practical purposes we may treat the exchange rate volatilities and correlations as observed rather than latent we do so and we characterize their joint distribution both unconditionally and conditionally noteworthy results include a simple normality inducing volatility transformation high contemporaneous correlation across volatilities high correlation between correlation and volatilities pronounced and persistent dynamics in volatilities and correlations evidence of long memory dynamics in volatilities and correlations and remarkably precise scaling laws under temporal aggregation

designing realised kernels to measure the ex post variation of equity prices in the presence of noise this paper shows how to use realised kernels to carry out efficient feasible inference on the expost variation of underlying equity prices in the presence of simple models of market frictions the issue is subtle with only estimators which have symmetric weights delivering consistent estimators with mixed gaussian limit theorems the weights can be chosen to achieve the best possible rate of convergence and to have an asymptotic variance which is close to that of the maximum likelihood estimator in the parametric version of this problem realised kernels can also be selected to i be analysed using endogenously spaced data such as that in databases on transactions ii allow for market frictions which are endogenous iii allow for temporally dependent noise the finite sample performance of our estimators is studied using simulation while empirical work illustrates their use in practice

long memory behavior of returns after intraday financial jumps abstract in this paper characterization of intraday financial jumps and time dynamics of returns after jumps is investigated and will be analytically and empirically shown that intraday jumps are power law distributed with the exponent 1 2 in addition returns after jumps show long memory behavior in the theory of finance it is important to be able to distinguish between jumps and continuous sample path price movements and this can be achieved by introducing a statistical test via calculating sums of products of returns over small period of time in the case of having jump the null hypothesis for normality test is rejected this is based on the idea that returns are composed of mixture of normally distributed and power law distributed data 1 r 1 probability of rejection of null hypothesis is a function of which is equal to one for 1 2 within large intraday sample size m to test this idea empirically we downloaded sp and it represents a power law exponent in 2015 2016 greater than one in 1997 1998 assuming that i i d returns generally follow poisson distribution if the jump is a causal factor high returns after jumps are the effect we show that returns caused by jump decay as power law distribution to test this idea empirically we average over the time dynamics of all days therefore the superposed time dynamics after jump represent a power law which indicates that there is a long memory with a power law distribution of return after jump

stabilization on zero error manifolds and the nonlinear servomechanism problem the extended linearization methodology is applied to the nonlinear servomechanism problem for the case of time varying exogenous signals this yields a novel approach to establishing exponential manifold known as the zero error manifold advantages of the approach are that the underlying theory is relatively simple and that a requirement of small derivatives for the exogenous signals is used rather than a requirement that the exogenous signals remain small thus certain cases of unbounded exogenous signals can be treated a transmission zero condition for existence of the requisite zero error manifold is given

external theory for stochastic processes abstract the purpose of this paper is to provide an overview of the asymptotic distributional theory of extreme values for a wide class of dependent stochastic sequences and continuous parameter processes the theory contains the standard classical extreme value results for maxima and extreme order statistics as special cases but is richer on account of the diverse behavior possible under dependence in both discrete and continuous time contexts emphasis is placed on stationary cases but other important classes e g mark of sequences are included significant ideas and methods are described rather than details and in particular the nature and role of important underlying point processes such as exceedances and upcrossings are emphasized applications are given to particular classes of process e g normal moving average and connections with related theory such as convergence of sums are indicated

spherical codes maximal local packing density and the golden ratio the densest local packing dlp problem in d dimensional euclidean space rd involves the placement of n nonoverlapping spheres of unit diameter near an additional fixed unit diameter sphere such that the greatest distance from the center of the fixed sphere to the centers of any of the n surrounding spheres is minimized solutions to the dlp problem are relevant to the realizability of pair correlation functions for packings of nonoverlapping spheres and might prove useful in improving upon the best known upper bounds on the maximum packing fraction of sphere packings in dimensions greater than 3 the optimal spherical code problem in rd involves the placement of the centers of n nonoverlapping spheres of unit diameter onto the surface of a sphere of radius r such that r is minimized it is proved that in any dimension all solutions between unity and the golden ratio to the optimal spherical code problem for n spheres are also solutions to the corresponding dlp problem it follows that for any packing

estimation of continuous time stochastic volatility models with jumps using high frequency data abstract this paper proposes a method of inference for general stochastic volatility models containing price jumps the estimation is based on treating realized multipower variation statistics calculated from high frequency data as their unobservable fill in asymptotic limits the paper provides easy to check conditions under which the error in estimation resulting from this approximation is o p 1 and additional ones under which it is o p 1 t where t is the number of days in the sample extensive monte carlo analysis shows that the proposed estimation method works well in finite samples provided asymptotic approximations are used the estimation technique is applied to the estimation of two semiparametric models

non gaussian ornstein uhlenbeck based models and some of their uses in financial economics non gaussian processes of ornstein uhlenbeck ou type offer the possibility of capturing important distributional deviations from gaussianity and for flexible modelling of dependence structures this paper develops this potential drawing on and extending powerful results from probability theory for applications in statistical analysis their power is illustrated by a sustained application of ou processes within the context of finance and econometrics we construct continuous time stochastic volatility models for financial assets where the volatility processes are superpositions of positive ou processes and we study these models in relation to financial data and theory

estimating tails of probability distributions we study the asymptotic properties of estimators of the tail of a distribution based on the excesses over a threshold a key idea is the use of pickands generalised pareto distribution and its fitting in most cases by the method of maximum likelihood the results cover all three limiting types of extreme value theory we propose a new estimator for an index of regular variation and show that it often performs better than hill s estimator we give new results for estimating the endpoint of a distribution extending earlier work by hall and by smith and weissman finally we give detailed results for the domain of attraction of exp e x and show that in most cases our proposed estimator is more efficient than two others one based on the exponential distribution and the other due to davis and resnick we also touch briefly on the problem of large deviations from a statistical point of view the results make extensive use of existing work on rates of convergence

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

testing whether jumps have finite or infinite activity we propose statistical tests to discriminate between the finite and infinite activity of jumps in a semimartingale discretely observed at high frequency the two statistics allow for a symmetric treatment of the problem we can either take the null hypothesis to be finite activity or infinite activity when implemented on high frequency stock returns both tests point toward the presence of infinite activity jumps in the data

estimation of jump tails we propose a new and flexible non parametric framework for estimating the jump tails of ito semimartingale processes the approach is based on a relatively simple to implement set of estimating equations associated with the compensator for the jump measure or its intensity that only utilizes the weak assumption of regular variation in the jump tails along with in fill asymptotic arguments for directly estimating the large jumps the procedure assumes that the large sized jumps are identically distributed but otherwise allows for very general dynamic dependencies in jump occurrences and importantly does not restrict the behavior of the small jumps nor the continuous part of the process and the temporal variation in the stochastic volatility on implementing the new estimation procedure with actual high frequency data for the s p 500 aggregate market portfolio we find strong evidence for richer and more complex dynamic dependencies in the jump tails than hitherto entertained in the literature