This paperc onsiders the problem o fnumerically evaluating barrier option prices when the dynamics of the underlying are driven by stochastic volatility following the square root process of Heston (1993). We develop a method of lines approach to evaluate the price as well as the delta and gamma...

This paper considers the problem of numerically evaluating American option prices when the dynamics of the underlying are driven by both stochastic volatility following the square root process of Heston (1993), and by a Poisson jump process of the type originally introduced by Merton (1976). We...

The following sections are included:The Model

The following sections are included:IntroductionProblem Statement — The Heston ModelFinding the Density Function using Integral TransformsSolution for the American Call OptionNumerical Scheme for the Free SurfaceConclusionAppendixProof of Proposition 5.8 — The European Option PriceEvaluation...

In this chapter we shall drop the stochastic volatility component from the dynamics by assuming that the variance is constant and merely discuss how to handle the jump term in the transform approach. Option pricing under jump-diffusion dynamics was originally investigated by Merton (1976) for...

This book has explored the pricing of American options. It has focused in particular on American call options but the techniques are generally applicable. We started in Chapter 2 with the case of the underlying asset dynamics following a jump-diffusion and stochastic volatility process…

The American option pricing problem has been explored in great depth in the option pricing literature. The survey by Barone-Adesi (2005) provides an overview of this research for the case of the American put under the classical Brownian motion process for asset returns…

In Chapter 3 we considered the simpler case of geometric Brownian motion plus jump-diffusion dynamics. In Chapter 4 we considered the case of stochastic volatility and jump-diffusion dynamics but in that case the volatility process was of the Heston type and the jumps were normally distributed....

The following sections are included:IntroductionThe Problem Statement — The Merton-Heston ModelThe Integral Transform SolutionThe Martingale RepresentationConclusionAppendixDeriving the Inhomogeneous PIDEVerifying Duhamel's PrincipleProof of Proposition 4.3 — Fourier Transform of the...

The Fourier cosine expansion approach (COS) is developed by Fang and Oosterlee (2008) using the Cosine series expansions of the value function at the next time level and the density function. The resulting equation is called the COS formula, due to the use of Fourier cosine series expansions....