Bivariate option pricing with copulas

In this paper we suggest the adoption of copula functions in order to price bivariate contingent claims. Copulas enable us to imbed the marginal distributions extracted from vertical spreads in the options markets in a multivariate pricing kernel. We prove that such kernel is a copula function, and that its super-replication strategy is represented by the Fréchet bounds. As applications, we provide prices for binary digital options, options on the minimum and options to exchange one asset for another. For each of these products, we provide no-arbitrage pricing bounds, as well as the values consistent with independence of the underlying assets. As a final reference value, we use a copula function calibrated on historical data. ∗The authors would like to thank an anonymous referee for useful comments that were of great help for the revision of the paper. The usual disclaimer applies. Corresponding author: Elisa Luciano, Dept. Statistics and Applied Mathematics, P.zza Arbarello 8, I-10121 Torino, e-mail:[email protected]