Arbitrage-Free Pricing of XVA | Hanlon Financial Systems Center

Arbitrage-Free Pricing of XVA

Arbitrage-Free Pricing of XVA

seminar date: 
Thursday, April 28, 2016 - 5:45pm
seminar location: 
Maxim Bichuch,Assistant Professor, Applied Math & Stats - Johns Hopkins University

We develop a framework for computing the total valuation adjustment (XVA) of a European claim accounting for funding costs, counterparty credit risk, and collateralization. Based on no-arbitrage arguments, we derive backward stochastic differential equations (BSDEs) associated with the replicating portfolios of long and short positions in the claim. This leads to the definition of buyer's and seller's XVA, which in turn identify a no-arbitrage interval. In the case that borrowing and lending rates coincide, we provide a fully explicit expression for the uniquely determined XVA, expressed as a percentage of the price of the traded claim, and for the corresponding replication strategies. In the general case of asymmetric funding, repo and collateral rates, we study the semi-linear partial differential equation (PDE) characterizing buyer's and seller's XVA and show the existence of a unique classical solution to it. To illustrate our results, we conduct a numerical stu  dy demonstrating how funding costs, repo rates, and counterparty risk contribute to determine the total valuation adjustment. This talk is based on joint works with Agostino Capponi (Columbia) and Stephan Sturm (WPI).




Maxim Bichuch holds a M.S. from NYU and a Ph.D. from CMU both in Financial Mathematics. He has been a Postdoctoral Research Associate & Lecturer in the ORFE department at Princeton, and an Assistant Professor at WPI, before joining the department of Applied Math & Stats at JHU as an Assistant Professor. Prior to obtaining his Ph.D. Maxim has also gained corporate experience working for Citigroup and Bear Stearns.