CVA and Vulnerable Options in Stochastic Volatility Models

33 Pages Posted: 2 Aug 2019

See all articles by Elisa Alos

Elisa Alos

University of Pompeu Fabra - Department of Economics

Fabio Antonelli

University of Rome I

Alessandro Ramponi

University of Rome Tor Vergata

Sergio Scarlatti

University of Rome Tor Vergata

Date Written: July 30, 2019

Abstract

In this work we want to provide a general principle to evaluate the CVA (Credit Value Adjustment) for a vulnerable option, that is an option subject to some default event, concerning the solvability of the issuer. CVA is needed to evaluate correctly the contract and it is particularly important in presence of WWR (Wrong Way Risk), when a credit deterioration determines an increase of the claim's price. In particular, we are interested in evaluating the CVA in stochastic volatility models for the underlying's price (which often fit quite well the market's prices) when admitting correlation with the default event. By cunningly using Ito's calculus, we provide a general representation formula applicable to some popular models such as SABR, Hull & White and Heston, which explicitly shows the correction in CVA due to the processes correlation. Later, we specialize this formula and construct its approximation for the three selected models. Lastly, we run a numerical study to test the formula's accuracy, comparing our results with Monte Carlo simulations.

Keywords: Credit Value Adjustment, Vulnerable Options, Stochastic volatility model, Intensity approach

JEL Classification: E43, G12, G13

Suggested Citation

Alos, Elisa and Antonelli, Fabio and Ramponi, Alessandro and Scarlatti, Sergio, CVA and Vulnerable Options in Stochastic Volatility Models (July 30, 2019). Available at SSRN: https://ssrn.com/abstract=3429088 or http://dx.doi.org/10.2139/ssrn.3429088

Elisa Alos

University of Pompeu Fabra - Department of Economics ( email )

c/o Ramon Trias Fargas 25-27
08005 Barcelona
Spain
34 93 542 19 25 (Phone)
34 93 542 17 46 (Fax)

Fabio Antonelli

University of Rome I ( email )

Piazzale Aldo Moro 5
Roma, Rome 00185
Italy

Alessandro Ramponi (Contact Author)

University of Rome Tor Vergata ( email )

Via di Tor Vergata
Rome, Lazio 00133
Italy

Sergio Scarlatti

University of Rome Tor Vergata ( email )

Via di Tor Vergata
Rome, Lazio 00133
Italy

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