Pricing Vulnerable Options with Copulas

ICER Working Paper, 2001

38 Pages Posted: 21 Feb 2002

See all articles by Elisa Luciano

Elisa Luciano

University of Turin - Department of Statistics and Applied Mathematics

Umberto Cherubini

University of Bologna - Department of Economics

Date Written: August 2001

Abstract

In this paper we apply a copula function pricing technique to the evaluation of vulnerable options, i.e. options with counterpart risk. Using copulas enables to separate the specification of marginal distributions and the dependence structure of the events of exercise of the option and default of the counterpart. Our proof that counterpart risk is evaluated as a copula function is based on no-arbitrage arguments only. This makes our results directly applicable to incomplete market models. Also, the no-arbitrage arguments provide easy-to-implement super-replication strategies. We study digital, call and put options with counterpart risk. Further, we price a credit derivative contract, namely a default put option. We calibrate the models on real market data, using a mixing copula, which provides closed form pricing formulas.

Keywords: Credit risk, vulnerable options, copula functions

JEL Classification: G12

Suggested Citation

Luciano, Elisa and Cherubini, Umberto, Pricing Vulnerable Options with Copulas (August 2001). ICER Working Paper, 2001, Available at SSRN: https://ssrn.com/abstract=286712 or http://dx.doi.org/10.2139/ssrn.286712

Elisa Luciano (Contact Author)

University of Turin - Department of Statistics and Applied Mathematics ( email )

Corso Unione Sovietica 218 bis
Turin, I-10122
Italy
+ 39 011 6705230 (Phone)

Umberto Cherubini

University of Bologna - Department of Economics ( email )

Strada Maggore, 45
Bologna, FI 40125
Italy
+ +39 051 2092615 (Phone)

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