### 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) |
---|---|

Pages (from-to) | 141-176 |

Number of pages | 36 |

Journal | Review of Derivatives Research |

Volume | 13 |

Issue number | 2 |

DOIs | |

State | Published - 2010 |

### Fingerprint

### 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

**Pricing swaps and options on quadratic variation under stochastic time change models-discrete observations case.** / Itkin, Andrey; Carr, Peter.

Research output: Contribution to journal › Article

*Review of Derivatives Research*, vol. 13, no. 2, pp. 141-176. https://doi.org/10.1007/s11147-009-9048-z

}

TY - JOUR

T1 - Pricing swaps and options on quadratic variation under stochastic time change models-discrete observations case

AU - Itkin, Andrey

AU - Carr, Peter

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

KW - Asymptotic method

KW - Closed-form solution

KW - Levy models

KW - Options

KW - Pricing

KW - Stochastic time change

KW - Variance swaps

KW - Volatility swaps

UR - http://www.scopus.com/inward/record.url?scp=77953323402&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77953323402&partnerID=8YFLogxK

U2 - 10.1007/s11147-009-9048-z

DO - 10.1007/s11147-009-9048-z

M3 - Article

VL - 13

SP - 141

EP - 176

JO - Review of Derivatives Research

JF - Review of Derivatives Research

SN - 1380-6645

IS - 2

ER -