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.
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We thank Arthur Sepp and an anonymous referee for useful comments. We assume full responsibility for any remaining errors.
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Itkin, A., Carr, P. Pricing swaps and options on quadratic variation under stochastic time change models—discrete observations case. Rev Deriv Res 13, 141–176 (2010). https://doi.org/10.1007/s11147-009-9048-z
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DOI: https://doi.org/10.1007/s11147-009-9048-z
Keywords
- Variance swaps
- Volatility swaps
- Options
- Levy models
- Stochastic time change
- Asymptotic method
- Closed-form solution
- Pricing