Financial/Actuarial Mathematics

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. Speaker(s): Roger Lee (University of Chicago)