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

Andrey Itkin, Peter Carr

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)141-176
Number of pages36
JournalReview of Derivatives Research
Volume13
Issue number2
DOIs
StatePublished - 2010

Fingerprint

Swaps
Quadratic variation
Pricing
Stochastic time change
Discrete model
Fair price
Contingent claims
Affine model
Characteristic function

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

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

In: Review of Derivatives Research, Vol. 13, No. 2, 2010, p. 141-176.

Research output: Contribution to journalArticle

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