Abstract This paper treats the risk-averse optimal portfolio problem with consumption in continuous time with a stochastic-volatility, jump-diffusion (SVJD) model of the underlying risky asset and the volatility. The new developments are the use of the SVJD model with double-uniform jump-amplitude distributions and time-varying market parameters for the optimal portfolio problem. Although unlim...

We consider the problem of valuation of certain Asian options in the geometric jump-diffusion models with continuously dividend-paying assets. With the sources of diffusion risks and two primitive tradeable assets, the market in this model is, in general, incomplete, and so, there are more than one equivalent martingale measures and no-arbitrage prices. For this jump-diffusion model, we adopt t...

In this paper, we present two efficient algorithms for pricing credit default swaps based on a structural default model. In our model, the value of the firm is assumed to be the exponential of a jump-diffusion process. Our first algorithm to price a credit default swap within this framework is an efficient and unbiased Monte Carlo simulation. An excellent performance is obtained by first simula...

We propose a new computational method for the valuation of options in jump-diffusion models. The option value function for European and barrier options satisfies a partial integrodifferential equation (PIDE). This PIDE is commonly integrated in time by implicit-explicit (IMEX) time discretization schemes, where the differential (diffusion) term is treated implicitly, while the integral (jump) t...

Birth-jump models are designed to describe population models for which growth and spatial spread cannot be decoupled. A birth-jump model is a nonlinear integro-differential equation. We present two different derivations of this equation, one based on a random walk approach and the other based on a two-compartmental reaction-diffusion model. In the case that the redistribution kernels are highly...

If the intensity parameter in a jump diffusion model is identically zero, then parameters characterizing the jump size density cannot be identified. In general, this lack of identification precludes consistent estimation of identified parameters. Hence, it should be standard practice to consistently pretest for jumps, prior to estimating jump diffusions. Many currently available tests have powe...

The main goal of this paper is to study market volatility risk premia. I develop a multifactor model by proposing a pricing kernel, where the market return, the diffusion volatility and the jump volatility are fundamental factors that change the investment opportunity set. Based on estimates of the diffusion and jump volatility factors using an enriched dataset including S&P500 index returns, i...

This paper proposes a Laplace-transform-based approach to price the fixed-strike quantile options as well as to calculate the associated hedging parameters (delta and gamma) under a hyperexponential jump diffusion model, which can be viewed as a generalization of the well-known Black–Scholes model and Kou’s double exponential jump diffusion model. By establishing a relationship between floating...

In this paper, the author discusses the distribution of the jump-diffusion CIR model (JCIR) and its applications in credit risk. Applying the piecewise deterministic Markov process theory and martingale theory, we first obtain the closed forms of the Laplace transforms for the distribution of the jump-diffusion CIR model and its integrated process. Based on the obtained Laplace transforms, we d...

This paper develops a tractable dynamic term structure models under jump-diffusion and regime shifts with time varying transition probabilities. The model allows for regime-dependent jumps while both jump risk and regime-switching risk are priced. Closed form solution for the term structure is obtained for an affine-type model under loglinear approximation. JEL Classification: G12, E43, E52