# Variance swaps on time-changed Markov processes

Roger Lee (University of Chicago), *March 28, 2019*

** Abstract: ** We prove that a variance swap has the same price as a co-terminal European-style contract, when the underlying is a Markov process, time-changed by a general continuous stochastic clock, which is allowed to have general correlation with the driving Markov process, which is allowed to have state-dependent jump distributions. The European contract’s payoff function satisfies an ordinary integro-differential equation, which depends only on the dynamics of the Markov process, not on the clock. In some examples, the payoff function that prices the variance swap can be computed explicitly. Joint work with Peter Carr and Matt Lorig.

* Roger Lee is Associate Professor of Mathematics at the University of Chicago. He also serves as an Associate Editor of Mathematical Finance and an Associate Editor of the SIAM Journal on Financial Mathematics. His research interests include robust pricing and hedging, implied volatility asymptotics, and volatility contracts. He has a Ph.D. from Stanford and a B.A. from Harvard. *