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Pricing Perpetual American Compound Options under a Matrix-Exponential Jump-Diffusion Model

Pricing Perpetual American Compound Options under a Matrix-Exponential Jump-Diffusion Model This paper considers the problem of pricing perpetual American compound options under a matrix-exponential jump-diffusion model. The rational prices of these options are defined as the value functions of the corresponding optimal stopping problems. The general optimal stopping theory and the averaging method for solving the optimal stopping problems are applied to find the value functions and the optimal stopping times and thereby to determine the rational prices and the optimal boundaries of these perpetual American compound options. Explicit formulae for the rational prices and the optimal boundaries are also obtained for hyper-exponential jump-diffusion models. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematical Finance Taylor & Francis

Pricing Perpetual American Compound Options under a Matrix-Exponential Jump-Diffusion Model

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Pricing Perpetual American Compound Options under a Matrix-Exponential Jump-Diffusion Model

Abstract

This paper considers the problem of pricing perpetual American compound options under a matrix-exponential jump-diffusion model. The rational prices of these options are defined as the value functions of the corresponding optimal stopping problems. The general optimal stopping theory and the averaging method for solving the optimal stopping problems are applied to find the value functions and the optimal stopping times and thereby to determine the rational prices and the optimal boundaries of...
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Publisher
Taylor & Francis
Copyright
© 2015 Taylor & Francis
ISSN
1466-4313
eISSN
1350-486X
DOI
10.1080/1350486X.2015.1118354
Publisher site
See Article on Publisher Site

Abstract

This paper considers the problem of pricing perpetual American compound options under a matrix-exponential jump-diffusion model. The rational prices of these options are defined as the value functions of the corresponding optimal stopping problems. The general optimal stopping theory and the averaging method for solving the optimal stopping problems are applied to find the value functions and the optimal stopping times and thereby to determine the rational prices and the optimal boundaries of these perpetual American compound options. Explicit formulae for the rational prices and the optimal boundaries are also obtained for hyper-exponential jump-diffusion models.

Journal

Applied Mathematical Finance – Taylor & Francis

Published: Nov 2, 2015

Keywords: Option pricing; perpetual American compound option; optimal stopping problem; jump-diffusion process

References

  • Russian and American Put Options under Exponential Phase-Type Lévy Models
  • Hedging Volatility Risk
  • The Valuation of Corporate Liabilities as Compound Options
  • The Valuation of Compound Options
  • Wiener-Hopf Factorization for Lévy Processes Having Positive Jumps with Rational Transforms
  • Optimal Stopping and Perpetual Options for Lévy Processes
  • On Optimal Stopping Problems for Matrix-Exponential Jump-Diffusion Processes
  • An Approach for Solving Perpetual Optimal Stopping Problems Driven by Lévy Processes