### Abstract

A model is developed for pricing volatility derivatives, such as variance swaps and volatility swaps under a continuous-time Markov-modulated version of the stochastic volatility (SV) model developed by Heston. In particular, it is supposed that the parameters of this version of Heston's SV model depend on the states of a continuous-time observable Markov chain process, which can be interpreted as the states of an observable macroeconomic factor. The market considered is incomplete in general, and hence, there is more than one equivalent martingale pricing measure. The regime switching Esscher transform used by Elliott et al. is adopted to determine a martingale pricing measure for the valuation of variance and volatility swaps in this incomplete market. Both probabilistic and partial differential equation (PDE) approaches are considered for the valuation of volatility derivatives.

Original language | English |
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Pages (from-to) | 41-62 |

Number of pages | 22 |

Journal | Applied Mathematical Finance |

Volume | 14 |

Issue number | 1 |

DOIs | |

Publication status | Published - Feb 2007 |

Externally published | Yes |

### Keywords

- Markov-modulated Heston's SV model
- Observable Markov chain process
- Regime switching Esscher transform
- Regime switching OU-process
- Variance swaps
- Volatility swaps

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## Cite this

*Applied Mathematical Finance*,

*14*(1), 41-62. https://doi.org/10.1080/13504860600659222