Pricing currency options under two-factor Markov-modulated stochastic volatility models

Tak Kuen Siu*, Hailiang Yang, John W. Lau

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

41 Citations (Scopus)

Abstract

This article investigates the valuation of currency options when the dynamic of the spot Foreign Exchange (FX) rate is governed by a two-factor Markov-modulated stochastic volatility model, with the first stochastic volatility component driven by a lognormal diffusion process and the second independent stochastic volatility component driven by a continuous-time finite-state Markov chain model. The states of the Markov chain can be interpreted as the states of an economy. We employ the regime-switching Esscher transform to determine a martingale pricing measure for valuing currency options under the incomplete market setting. We consider the valuation of the European-style and American-style currency options. In the case of American options, we provide a decomposition result for the American option price into the sum of its European counterpart and the early exercise premium. Numerical results are included.

Original languageEnglish
Pages (from-to)295-302
Number of pages8
JournalInsurance: Mathematics and Economics
Volume43
Issue number3
DOIs
Publication statusPublished - Dec 2008
Externally publishedYes

Keywords

  • Currency options
  • Decomposition
  • Esscher transform
  • Regime switching
  • Two-factor stochastic volatility

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