Multivariate option pricing with copulas

Abstract: In this paper we suggest the adoption of copula functions in order
to price multivariate 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
fucntion, 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 …nal reference value, we use a copula function calibrated on historical
data.

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