### 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 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 |

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### Keywords

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

### Cite this

*Annals of Finance*,

*1*(4), 423-432. https://doi.org/10.1007/s10436-005-0013-z

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*Annals of Finance*, vol. 1, no. 4, pp. 423-432. https://doi.org/10.1007/s10436-005-0013-z

**Option pricing and Esscher transform under regime switching.** / Elliott, Robert J.; Chan, Leunglung; Siu, Tak Kuen.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Option pricing and Esscher transform under regime switching

AU - Elliott, Robert J.

AU - Chan, Leunglung

AU - Siu, Tak Kuen

PY - 2005/10

Y1 - 2005/10

N2 - 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.

AB - 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.

KW - Esscher transform

KW - Hidden Markov chain model

KW - MEMM

KW - Option pricing

KW - Regimes witching

UR - http://www.scopus.com/inward/record.url?scp=24144486570&partnerID=8YFLogxK

U2 - 10.1007/s10436-005-0013-z

DO - 10.1007/s10436-005-0013-z

M3 - Article

VL - 1

SP - 423

EP - 432

JO - Annals of Finance

JF - Annals of Finance

SN - 1614-2446

IS - 4

ER -