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

Andrey Itkin, Peter Carr

Research output: Contribution to journalArticle


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 languageEnglish (US)
Pages (from-to)141-176
Number of pages36
JournalReview of Derivatives Research
Issue number2
StatePublished - Jan 1 2010



  • 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)

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