Pricing variance swaps on time-changed Markov processes

Peter Carr, Roger Lee, Matthew Lorig

Research output: Contribution to journalArticlepeer-review


We prove that the variance swap rate (fair strike) equals the price of a co-terminal European-style contract when the underlying is an exponential Markov process, time-changed by an arbitrary continuous stochastic clock, which has arbitrary correlation with the driving Markov process, provided that the payoff function G of the European contract satisfies an ordinary integro-differential equation, which depends only on the dynamics of the Markov process, not on the clock. We present examples of Markov processes where the function G that prices the variance swap can be computed explicitly. In general, the solutions G are not contained in the logarithmic family previously obtained in the special case where the Markov process is a Lévy process.

Original languageEnglish (US)
Pages (from-to)672-689
Number of pages18
JournalSIAM Journal on Financial Mathematics
Issue number2
StatePublished - 2021


  • Integro-differential
  • Markov process
  • Time change
  • Variance swap

ASJC Scopus subject areas

  • Numerical Analysis
  • Finance
  • Applied Mathematics


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