Abstract. In this article we extend earlier work on the jump-diffusion risk-sensitive asset management problem in a factor model [SIAM J. Fin. Math. 2 (2011) 22-54] by allowing jumps in both the factor process and the asset prices, as well as stochastic volatility and investment constraints. In this case, the HJB equation is a partial integro-differential equation (PIDE). We are able to show th...

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...

Jump diffusion processes are often used as an alternative to geometric Brownian motion within continuous–time dynamic financial time series models. The advantages of the jump diffusion process are that it can not only account for discrete jumps in the path of the process, but it also provides a simple way of replacing the Gaussian return distributions that arise in geometric Brownian motion mod...

Risk management is an important issue when there is a catastrophic event that affects asset price in the market such as a sub-prime financial crisis or other financial crisis. By adding a jump term in the geometric Brownian motion, the jump diffusion model can be used to describe abnormal changes in asset prices when there is a serious event in the market. In this paper, we propose an importanc...

If the price of an asset follows a jump diffusion process, the market is in general incomplete. In this case, hedging a contingent claim written on the asset is not a trivial matter, and other instruments besides the underlying must be used to hedge in order to provide adequate protection against jump risk. We devise a dynamic hedging strategy that uses a hedge portfolio consisting of the under...

This paper aims at extending the analytical tractability of the Black-Scholes model to alternative models with arbitrary jump size distributions. More precisely, we propose a jump diffusion model for asset prices whose jump sizes have a mixed-exponential distribution, which is a weighted average of exponential distributions but with possibly negative weights. The new model extends existing mode...

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...

We develop and analyze a class of unbiased Monte Carlo estimators for multivariate jump-diffusion processes with state-dependent drift, volatility, jump intensity size. A change measure argument is used to extend existing the inter-arrival diffusion include jumps. Under standard regularity conditions on coefficient target functions, we prove unbiasedness finite variance properties resulting est...

Futures contract is one of the most important derivatives that is used in financial markets in all over the world to buy or sell an asset or commodity in the future. Pricing of this tool depends on expected price of asset or commodity at the maturity date. According to this, theoretical futures pricing models try to find this expected price in order to use in the futures contract. So in this ar...

Consider a nonsymetric generalized diffusion X(·) in R d generated by the differential operator A(x) = ij ∂iaij(x)∂j + i bi(x)∂i. In this paper the diffusion process is approximated by Markov jump processes Xn(·) in homogeneous and isotropic grids Gn ⊂ R d which converge in distribution to diffusion. The generators of Xn(·) are constructed explicitly. Due to the homogeneity and isotropy of grid...