Option pricing and Esscher transform under regime switching

Robert J. Elliott, Leunglung Chan, Tak Kuen Siu

Research output: Contribution to journalArticle

Abstract

We consider the option pricing problem when the risky underlying assets are driven by Markov-modulated Geometric Brownian Motion (GBM). That is, the market parameters, for instance, the market interest rate, the appreciation rate and the volatility of the underlying risky asset, depend on unobservable states of the economy which are modelled by a continuous-time Hidden Markov process. The market described by the Markov-modulated GBM model is incomplete in general and, hence, the martingale measure is not unique. We adopt a regime switching random Esscher transform to determine an equivalent martingale pricing measure. As in Miyahara [33], we can justify our pricing result by the minimal entropy martingale measure (MEMM). © Springer-Verlag 2005.

Original languageEnglish
Pages (from-to)423-432
Number of pages10
JournalAnnals of Finance
Volume1
Issue number4
DOIs
Publication statusPublished - Oct 2005

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Option pricing
Regime switching
Esscher transform
Assets
Geometric Brownian motion
Pricing
Minimal entropy martingale measure
Martingale
Continuous time
Martingale measure
Interest rates
Markov process

Keywords

  • Esscher transform
  • Hidden Markov chain model
  • MEMM
  • Option pricing
  • Regimes witching

Cite this

Elliott, Robert J. ; Chan, Leunglung ; Siu, Tak Kuen. / Option pricing and Esscher transform under regime switching. In: Annals of Finance. 2005 ; Vol. 1, No. 4. pp. 423-432.
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Option pricing and Esscher transform under regime switching. / Elliott, Robert J.; Chan, Leunglung; Siu, Tak Kuen.

In: Annals of Finance, Vol. 1, No. 4, 10.2005, p. 423-432.

Research output: Contribution to journalArticle

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