In this paper I analyze a broad class of continuous-time jump diffusion models of asset returns. In the models, stochastic volatility can arise either from a diffusion part, or a jump part, or both. The jump component includes either compound Poisson or Lévy α-stable jumps. To be able to estimate the models with latent Lévy α−stable jumps, I construct a new Markov chain Monte Carlo algorithm. I...

A computational solution is found for a optimal consumption and portfolio policy problem in which the underlying stock satisfies a geometric jump–diffusion in which both the diffusion and jump amplitude are log– normally distributed. The optimal objective is to maximize the expected, discounted utility of terminal wealth and the cumulative discounted utility of instantaneous consumption. The ju...

A computational solution is found for a optimal consumption and portfolio policy problem in which the underlying stock satisfies a geometric jump–diffusion in which both the diffusion and jump amplitude are log–normally distributed. The optimal objective is to maximize the expected, discounted utility of terminal wealth and the cumulative discounted utility of instantaneous consumption. The jum...

We present an approach to Bayesian model selection for finitely observed diffusion processes. We use data augmentation by treating the paths between observed points as missing data. For a fixed model formulation, the strong dependence between the missing paths and the volatility of the diffusion can be broken down by adopting the method of Roberts & Stramer (2001). We describe how this method m...

In this paper, we provide Laplace transform-based analytical solutions to pricing problems of various occupation-time-related derivatives such as step options, corridor options, and quantile options under Kou’s double exponential jump diffusion model. These transforms can be inverted numerically via the Euler Laplace inversion algorithm, and the numerical results illustrate that our pricing met...

It is well documented that a model for the underlying asset price process that seeks to capture the behaviour of the market prices of vanilla options needs to exhibit both diffusion and jump features. In this paper we assume that the asset price process S is Markov with càdlàg paths and propose a scheme for computing the law of the realized variance of the log returns accrued while the asset wa...

The first passage time (FPT) problem is ubiquitous in many applications. In finance, we often have to deal with stochastic processes with jump-diffusion, so that the FTP problem is reducible to a stochastic differential equation with jump-diffusion. While the application of the conventional Monte-Carlo procedure is possible for the solution of the resulting model, it becomes computationally ine...

We investigate “jump memory” using an extensive data base of short-term S&P 500 Index options. Jump memory refers to the attenuation of the implied jump intensity and magnitude parameters following a jump event. Behavioral and rational explanations for parameter attenuation are posited. A genetic algorithm is used to obtain implied parameter estimates. The pricing accuracy of the jump-diffusion...

Abstract:Accommodating exchange rate factors as exogenous disturbance, this paper proposes a mixed GARCH-Jump model to compares in general the volatility properties of returns series of the Shanghai composite index with those of the Dow Jones index. It also incorporates the asymmetry, clustering and leptokurtosis and fat-tail properties of returns volatility into an integrated analytic frame of...

The correlation factor for impurity diffusion by a vacancy-mechanism is a function of the vacancy-jump frequencies in the surroundings of the diffusing atom. Since in Si and Ge the vacancy can act as an acceptor, a long-range Coulomb interaction between donor atoms and vacancies exists. The usual assumption, that only a few vacancy-jump frequencies in the im­ mediate surroundings of the vacancy...