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A Regime-Switching Model for European Options

In: Stochastic Processes, Optimization, and Control Theory: Applications in Financial Engineering, Queueing Networks, and Manufacturing Systems

Author

Listed:
  • David D. Yao

    (Columbia University)

  • Qing Zhang

    (University of Georgia)

  • Xun Yu Zhou

    (The Chinese University of Hong Kong)

Abstract

We study the pricing of European-style options, with the rate of return and the volatility of the underlying asset depending on the market mode or regime that switches among a finite number of states. This regime-switching model is formulated as a geometric Brownian motion modulated by a finite-state Markov chain. With a Girsanov-like change of measure, we derive the option price using risk-neutral valuation. We also develop a numerical approach to compute the pricing formula, using a successive approximation scheme with a geometric rate of convergence. Using numerical examples of simple, two- or three-state Markov chain models, we are able to demonstrate the presence of the volatility smile and volatility term structure.

Suggested Citation

  • David D. Yao & Qing Zhang & Xun Yu Zhou, 2006. "A Regime-Switching Model for European Options," International Series in Operations Research & Management Science, in: Houmin Yan & George Yin & Qing Zhang (ed.), Stochastic Processes, Optimization, and Control Theory: Applications in Financial Engineering, Queueing Networks, and Manufacturing Systems, chapter 0, pages 281-300, Springer.
    • Handle: RePEc:spr:isochp:978-0-387-33815-6_14
    DOI: 10.1007/0-387-33815-2_14
    as

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