Vulnerable from Copulas ∗ Umberto Cherubini University of Bologna and ICER, Turin Elisa Luciano University of Turin and ICER, Turin December 2001 0.0.1 Motivation: coupling asset pricing and credit risk models The recent Enron case has brought to the centre of discussion the question of counterpart risk in derivative transactions, and the issue of correlation between derivative exposure and the main business of the counterpart. Is it wise to buy options on some underlying asset from counterparts that structurally have large exposures to it? A point is that they certainly know the business and the market better than other counterparts around. The bad news is that their exposure to the market of the underlying may cause them to default on their derivative obligation. For instance, buying a put option on a power derivative from a counterpart whose production may be severely hampered by a decrease in electricity prices leaves the long end of the contract exposed to default of the counterpart. In fact, the long end loses under the event against which the protection was sought in the first place, i.e. a decrease in electricity prices. By the same token, buying protection against default of an Argentinian obligor from an Argentinian bank may not turn out to be most effective way to reduce credit risk. The pricing of vulnerable derivatives, i.e. derivatives exposed to default of the counterpart, has been the object of a large literature. All of this literature has focused on specific pricing approaches. The typical model is a Black and Scholes setting for the underlying asset and a structural or reduced form model for the default probability of the counterpart. As for the modelling of the underlying asset, it is well known that current op- tion pricing techniques are far beyond the standard Black and Scholes formulas, and try to account for smile and term structure effects of the volatility surface, as well as for market liquidity. The latter problem is particularly relevant in OTC transactions, which are typically based on non-standardized products, and it is for these same transactions that counterpart risk is also relevant. ∗ The Authors wish to thank the Editor and two anonymous referees for helpful suggestions. The usual disclaimers apply. 1