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

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  • Ming-Chi Chang
  • Yuan-Chung Sheu
  • Ming-Yao Tsai

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.

Suggested Citation

  • Ming-Chi Chang & Yuan-Chung Sheu & Ming-Yao Tsai, 2015. "Pricing Perpetual American Compound Options under a Matrix-Exponential Jump-Diffusion Model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 22(6), pages 553-575, December.
    • Handle: RePEc:taf:apmtfi:v:22:y:2015:i:6:p:553-575
    DOI: 10.1080/1350486X.2015.1118354
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    References listed on IDEAS

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    1. Carl Chiarella & Boda Kang, 2009. "The Evaluation of American Compound Option Prices Under Stochastic Volatility Using the Sparse Grid Approach," Research Paper Series 245, Quantitative Finance Research Centre, University of Technology, Sydney.
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    4. Geske, Robert, 1977. "The Valuation of Corporate Liabilities as Compound Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 541-552, November.
    5. Ernesto Mordecki, 2002. "Optimal stopping and perpetual options for Lévy processes," Finance and Stochastics, Springer, vol. 6(4), pages 473-493.
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