PhiMac Seminar - Weijie Pang - XVA Valuation under Market Illiquidity
Speaker: Weijie Pang (McMaster University)
Title: XVA Valuation under Market Illiquidity
Abstract: Before the 2008 financial crisis, most research in financial mathematics focused on pricing options without considering the effects of counterparties' default, illiquidity problems, and the role of the repurchase agreement (Repo) market. Recently, models were proposed to address this by computing the total valuation adjustment (XVA) of derivatives; however without considering a potential crisis in the market. In this article, we include a possible crisis by using an alternating renewal process to describe the switching between a normal financial regime and a financial crisis. We develop a framework for pricing the XVA of a European claim in this state-dependent framework. The price is characterized as a solution to a backward stochastic differential equation (BSDE), and we prove the existence and uniqueness of this solution. In a numerical study based on a deep learning algorithm for BSDEs, we compare the effect of different parameters on the valuation of the XVA.