We show how the value of a finite-lived option can be interpreted as the limit of a sequence of perpetual option values subject to default risk. This interpretation yields new closed form approximations for European and American option values in the Black Scholes model. Numerical results...

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…

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...