Quanto Pricing with Copulas

Abstract

“Valuing a derivative that depends on more than one underlying asset, like a currency quanto, which pays off in one currency based on the exchange rate between two others, requires knowledge of the correlation structure among them. Pricing is not difficult if one knows the joint probability distribution. But calibrating a pricing model to the market is much harder, because it requires an implied distribution that is simultaneously consistent with quanto prices and also with the volatility smiles from plain vanilla options in the underlying currencies. Recent work on copulas offers a start. Univariate distributions for the individual underlying assets (the “marginals”) can be obtained from plain vanilla options and then combined, using a copula function, into a joint distribution with whatever dependence structure is desired. But things are still not easy, because the common copula functions used in the finance literature do not have enough flexibility to match the actual implied distributions. In this article, Bennett and Kennedy offer a neat and easily implemented solution, in the form of a procedure for modifying the normal copula to produce realistic dependence structures. The ability to match a quanto volatility smiles is significantly enhanced, relative to the current standard procedure in the market.”