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....

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...

Margrabe provides a pricing formula for an exchange option where the distributions of both stock prices are log-normal with correlated components. Merton has provided a formula for the price of a European call option on a single stock where the stock price process contains a compound Poisson...

We consider the American option pricing problem in the case where the underlying asset follows a jump-diffusion process. We apply the method of Jamshidian to transform the problem of solving a homogeneous integro-partial differential equation (IPDE) on a region restricted by the early exercise...

This paper considers the problem of pricing American options when the dynamics of the underlying are driven by both stochastic volatility following a square-root process as used by Heston [<italic>Rev. Financial Stud.</italic>, 1993, <bold>6</bold>, 327--343], and by a Poisson jump process as introduced by Merton [<italic>J....</italic>

This paper presents a generalisation of McKean's free boundary value problem for American options by considering an American strangle position, where the early exercise of one side of the payoff will knock-out the out-of-the-money side. When attempting to evaluate the price of this American...