## 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).

Original language | English |
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Pages (from-to) | 423-432 |

Number of pages | 10 |

Journal | Annals of Finance |

Volume | 1 |

Issue number | 4 |

DOIs | |

Publication status | Published - Oct 2005 |

Externally published | Yes |

## Keywords

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