Everything You Always Wanted to Know About XVA Model Risk but Were Afraid to Ask

Abstract: Valuation adjustments, collectively named XVA, play an important role in modern derivatives pricing to take into account additional price components such as counterparty and funding risk premia. They are an exotic price component carrying a significant model risk and computational effort even for vanilla trades. We adopt an industry-standard realistic and complete XVA modelling framework, typically used by XVA trading desks, based on multi-curve time-dependent volatility G2++ stochastic dynamics calibrated on real market data, and a multi-step Monte Carlo simulation including both variation and initial margins. We apply this framework to the most common linear and non-linear interest rates derivatives, also comparing the MC results with XVA analytical formulas. Within this framework, we identify the most relevant model risk sources affecting the precision of XVA figures and we measure the corresponding computational effort. In particular, we show how to build a parsimonious and efficient MC time simulation grid able to capture the spikes arising in collateralized exposure during the margin period of risk. As a consequence, we also show how to tune accuracy vs performance, leading to sufficiently robust XVA figures in a reasonable time, a very important feature for practical applications. Furthermore, we provide a quantification of the XVA model risk stemming from the existence of a range of different parameterizations according to the EU prudent valuation regulation. Finally, this work also serves as an handbook containing step-by-step instructions for the implementation of a complete, realistic and robust modelling framework of collateralized exposure and XVA.