American Option Prices under Stochastic Volatility and Jump-Diffusion Dynamics — The Transform Approach

Carl Chiarella, Boda Kang and Gunter H. Meyer

Chapter 4 in The Numerical Solution of the American Option Pricing Problem:Finite Difference and Transform Approaches, 2014, pp 49-91 from World Scientific Publishing Co. Pte. Ltd.

Abstract: 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 PIDEProof of Proposition 4.4 — Laplace Transform of the PDE (4.14)Proof of Proposition 4.5 — Solving the PDE (4.17)Proof of Proposition 4.6 — Inverting the Laplace TransformProof of Proposition 4.7 — Inverting the Fourier TransformProof of Proposition 4.8 — Deriving the Price for a European CallDeriving the Early Exercise Premium

Keywords: American Option; Early Exercise; Method of Lines; Finite Difference Approach; Integral Transform Approach; Numerical Methods (search for similar items in EconPapers)
Date: 2014
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