Pricing Variance Swaps on Time-Changed Markov Processes

Peter Carr, Roger Lee and Matthew Lorig

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Abstract: 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 L\'evy process.

Date: 2017-05, Revised 2019-11
New Economics Papers: this item is included in nep-rmg
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