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...

We consider reflected jump-diffusions in the orthant R + with timeand state-dependent drift, diffusion and jump-amplitude coefficients. Directions of reflection upon hitting boundary faces are also allow to depend on time and state. Pathwise comparison results for this class of processes are provided, as well as absolute continuity properties for their associated regulator processes responsible...

This paper studies monotonicity and convexity properties of option prices in jump-diffusion models. In such models it is possible for a monotone contract function to give rise to an option price which is non-monotone in the underlying asset. This is connected to the fact that the no-crossing property, which holds for one-dimensional diffusions, may fail in the presence of jumps. We present a si...

By introducing the Jump-Diffusion Process and Markov Regime Shift, the paper explores Monte Carlo simulation to examine the pricing problem of single name Credit Default Swaps (CDS), which the price of CDS is affected by both unpredictable idiosyncratic risk and system risk caused by the macroeconomic change. The study shows that the price of CDS increases as the intensity and the amplitude of ...

The goal of this paper is to show that the jump-diffusion models are an essential and easy-to-learn tool for option pricing and risk management, and that they provide an adequate description of stock price fluctuations and market risks. We try to give an overview of the field without focusing on technical details. After introducing several widely used jump-diffusion models, we discuss Fourier t...

In recent years the financial world has focused on accurate pricing of exotic and hybrid products that are based on a combination of underlyings from different asset classes. In this paper we present an extension of the stochastic volatility models by a stochastic Hull-White interest rate component. It is our goal to include this system of stochastic differential equations in the class of affin...