Arbitrage-Free Pricing of XVA Part II: PDE Representation and Numerical Analysis

Arbitrage-Free Pricing of XVA – Part II: PDE Representation and Numerical Analysis

We study the semilinear partial differential equation (PDE) associated with the non-linear BSDE characterizing buyer’s and seller’s XVA in a framework that allows for asymmetries in funding, repo and collateral rates, as well as for early contract termination due to counterparty credit risk. We show the existence of a unique classical solution to the PDE by first proving the existence and uniqu...

Arbitrage-free pricing of XVA

Arbitrage-Free Pricing of XVA – Part I: Framework and Explicit Examples

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 noarbitrage arguments, we derive a nonlinear backward stochastic differential equation (BSDE) associated with the replicating portfolios of long and short positions in the claim. This leads to the definition of buye...

Two-Part Pricing with Costly Arbitrage

This paper considers the optimal two-part pricing strategy of a monopolist whose customers collude when they purchase the firm's product. In contrast to the sentiment in the existing price discrimination literature, I find that a monopolist's profit can actually increase when consumers share its good. When transaction costs for collusion are zero the firm can extract the full consumer surplus t...

PDE , Part II

1.1 Shocks and the Rankine-Hugoniot condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 Hopf’s treatment of Burgers equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3 Two basic examples of Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.4 Entropies and Admissibility Criteria . . . . ...