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

In: The Numerical Solution of the American Option Pricing Problem Finite Difference and Transform Approaches

Author

Listed:
  • Carl Chiarella
  • Boda Kang
  • Gunter H. Meyer

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

Suggested Citation

  • Carl Chiarella & Boda Kang & Gunter H. Meyer, 2014. "American Option Prices under Stochastic Volatility and Jump-Diffusion Dynamics — The Transform Approach," World Scientific Book Chapters, in: The Numerical Solution of the American Option Pricing Problem Finite Difference and Transform Approaches, chapter 4, pages 49-91, World Scientific Publishing Co. Pte. Ltd..
  • Handle: RePEc:wsi:wschap:9789814452625_0004
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