Arbitrage-Free Pricing of XVA – Part I: Framework and Explicit Examples
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چکیده
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 buyer’s and seller’s XVA, which in turn identify a no-arbitrage interval. When borrowing and lending rates coincide we provide a fully explicit expression for the uniquely determined price of XVA, expressed as a percentage of the price of the traded claim, and for the corresponding replication strategies. This extends the result of Piterbarg (2010) by incorporating the effect of premature contract termination due to default risk of the trader and of his counterparty.
منابع مشابه
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...
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تاریخ انتشار 2015