|Date: Wednesday, April 18, 2018
Location: 1866 East Hall (4:00 PM to 5:00 PM)
Title: Robust XVA
Abstract: We develop a framework for computing the robust valuation adjustment (XVA) of a credit swap portfolio traded between an investor and a risky counterparty. Based on no-arbitrage arguments, we derive a backward stochastic differential equation (BSDE) associated with the XVA of portfolio under a threshold copula model correlative the default times of investor, counterparty, and reference entities of the credit swaps in the portfolio. We compute the maximum and minimum XVA of the portfolio, which provides the interval in which the true (unknown) XVA lies. In the case that borrowing and lending rates coincide, we provide a fully explicit expression for the robust XVA bounds, and for the corresponding replication strategies in corporate bonds. In the general case of asymmetric funding, repo and collateral rates, we study the nonlinear ordinary differential equations (ODE) characterizing $\XVA$ and show the existence of a unique classical solution to it. To illustrate our results, we conduct a numerical study demonstrating how funding costs, counterparty risk and default risk uncertainty contribute to determine the total valuation adjustment.
This is a joint work with Agostino Capponi (Columbia University) and Stephan Sturm (Worcester Polytechnic Institute).
Speaker: Maxim Bichuch
Institution: Johns Hopkins