CVA and vulnerable options pricing by correlation expansions

We consider the problem of computing the credit value adjustment (CVA) of a European option in presence of the wrong way risk in a default intensity setting. Namely we model the asset price evolution as solution to a linear equation that might depend on different stochastic factors and we provide an approximate evaluation of the option's price, by exploiting a correlation expansion approach, introduced in Antonelli and Scarlatti (Finance Stoch 13:269-303, 2009). We also extend our theoretical analysis to include some further value adjustments, for instance due to collateralization and funding costs. Finally, in the CVA case, we compare the numerical performance of our method with the one recently proposed by Brigo and Vrins (Eur J Oper Res 269:1154-1164, 2018) and Brigo et al. (Innovations in insurance, risk and asset management, WSPC proceedings, 2018), in the case of a call option driven by a GBM correlated with a CIR default intensity. We additionally compare with the numerical evaluations obtained by other methods.