Multi-asset Stochastic Local Variance Contracts

Variance swaps now trade actively over-the-counter (OTC) on both stocks and stock indices. Also trading OTC are variations on variance swaps which localize the payoff in time, in the underlying asset price, or both. Given that the price of the underlying asset evolves continuously over time, it is well known that there exists a semi-robust hedge for these localized variance contracts. Remarkably, the hedge succeeds even though the stochastic process describing the instantaneous variance is never specified. In this paper, we present a generalization of these results to the case of two or more underlying assets. 1. We would like to acknowledge helpful comments from two referees, Bruno Dupire, Dilip Madan, and Tai-Ho Wang. Some of this work was completed while the second author was a visiting scholar at the Courant Institute. Multi-asset Stochastic Local Variance