XVA Hedging : Measuring its Performance and Risks via Discrete-Time Simulations

In this article we explore different hedging options for an XVA book: this topic is of practical interest given that accounting principles make it compulsory for financial institutions to account for CVA and DVA in their balance sheet, generating income volatility. Further, capital requirements for counterparty risk-intensive trades have been introduced by the Basel II and Basel III frameworks. To make things even more complicated some primary financial institutions have started accounting for the funding adjustment (FVA).All these aspects interact in a complex way and make it impossible to suggest a one-fits-all recipe. We propose to explore the effects of different hedging strategies via discrete-time hedging simulations, which in turn require the computation of the XVA and their risks for many time steps and many simulations in order to achieve convergence. No simulation-based XVA model could realistically be used for these purposes, given that it would be too resource-intensive: therefore we explore and develop the theory of approximated closed forms for XVA, ignoring wrong-way risk.We show some results from the discrete-time simulations that are encouraging and let one back her/his educated guesses with some quantitative evidence. The author wishes to thank prof. Damiano Brigo, Lorenzo Cornalba and Antonio Calabrese for the useful exchanges of opinions on the subject