### Abstract

We use a forward characteristic function approach to price variance and volatility swaps and options on swaps. The swaps are defined via contingent claims whose payoffs depend on the terminal level of a discretely monitored version of the quadratic variation of some observable reference process. As such a process we consider a class of Levy models with stochastic time change. Our analysis reveals a natural small parameter of the problem which allows a general asymptotic method to be developed in order to obtain a closed-form expression for the fair price of the above products. As examples, we consider the CIR clock change, general affine models of activity rates and the 3/2 power clock change, and give an analytical expression of the swap price. Comparison of the results obtained with a familiar log-contract approach is provided.

Original language | English (US) |
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Pages (from-to) | 141-176 |

Number of pages | 36 |

Journal | Review of Derivatives Research |

Volume | 13 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 2010 |

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### Keywords

- Asymptotic method
- Closed-form solution
- Levy models
- Options
- Pricing
- Stochastic time change
- Variance swaps
- Volatility swaps

### ASJC Scopus subject areas

- Finance
- Economics, Econometrics and Finance (miscellaneous)

### Cite this

*Review of Derivatives Research*,

*13*(2), 141-176. https://doi.org/10.1007/s11147-009-9048-z