Structural pricing of XVA metrics with stochastic recovery rates

In recent years counterparty credit risk (CCR) and valuation adjustments (XVA) dramatically changed both derivative pricing and risk management paradigms. Since the beginning of the global financial crisis, it became clear that high creditworthiness institutions could not be considered default-free any more. CCR is the risk which economic agents face due to the possible default of their over the counter (OTC) counterparts occurring prior to the full compliance of contractual payments. Since no financial or corporate entity can be considered entirely default-free any more, CCR affects bilaterally OTC trades. XVA is the growing family of valuation adjustments due to CCR and other risks related to funding and collateral margining.

The goal of this work is to jointly address the topics of CCR and XVA through a common structural approach for default modeling. In particular, we address a structural approach in which bankruptcy is modeled as the first-passage time of firm equity value from a predetermined lower barrier. Moreover, the numerical computation of the XVA for bilateral CCR in the context of energy commodities OTC derivatives contracts was performed. Furthermore, state-dependent stochastic recovery rates were introduced to analyze the impact on CCR.

A simple procedure to model state-dependent stochastic recovery rates, which reflects the severity of occurred defaults in terms of relative distance from the default barrier, is implemented. Furthermore, the relationship between the underlying volatility and the expected value of stochastic recoveries is highlighted. A sensitivity analysis of pure CCR adjustments with respect to credit and volatility shocks is performed to check some interesting asymptotic patterns. The model is calibrated on market data. In particular, the calibration of the main risk drivers, option prices quoted at the Chicago Mercantile Exchange were used. Furthermore, for credit risk estimation, Credit Default Swaps quotes of corporations included in the iTraxx Index were used, together with Euro OverNight Index Average (EONIA) rates for calibrating the term structure of interest rates at shortest maturities.