Abstracts

The aim of the paper is to provide a valuation framework for counterparty credit risk based on a structural default approach à la Merton which incorporates jumps and dependence between the assets of interest. In this model default is caused by the firm value falling below a prespecified threshold following unforeseeable shocks, which deteriorate its liquidity and ability to meet its liabilities. The presence of dependence between names captures wrong-way risk and right-way risk effects. The structural model traces back to Merton (1974), who considered only the possibility of default occurring at the maturity of the contract; first passage time models starting from the seminal contribution of Black and Cox (1976) extend the original framework to incorporate default events at any time during the lifetime of the contract. However, as the driving risk process used is the Brownian motion, all these models suffers of vanishing credit spreads over the short period - a feature not observed in reality. As a consequence, the CVA would be underestimated for short term deals as well as the so-called gap risk, i.e. the unpredictable loss due to a jump event in the market. Improvements aimed at resolving this issue include for example random default barriers and time dependent volatilities, and jumps. Hence, we adopt Lévy processes and capture dependence via a linear combination of two independent Lévy processes representing respectively the systematic risk factor and the idiosyncratic shock. We then apply this framework to the valuation of CVA and DVA related to equity contracts such as forwards and swaps. We analyse in details the case in which the driving process is a parsimonious non Gaussian process, such as the Normal Inverse Gaussian (NIG) one: this choice is motivated by the fact that the NIG process allows for skewness, excess kurtosis and a fairly rich jump dynamics although parsimonious in terms of number of parameters involved and calibration. We also compare against the results originated by the standard Gaussian assumption. The main focus is on the impact of correlation between entities on the value of CVA and DVA, with particular attention to wrong-way risk and right-way risk; this is explored via sensitivity analysis. Particular attention is also devoted to model calibration to market data; an empirical analysis is also conducted to evaluate how the cost of bilateral counterparty credit risk has varied over time.