A Complete XVA Valuation Framework

Why the “Law of One Price” is dead

Pricing a book of derivatives has become quite a complicated task, even when those derivatives are simple in nature. This is the effect of the new trading environment, highly dominated by credit, funding and capital costs. In this paper the author formally sets up a global valuation framework that accounts for market risk (risk neutral price), credit risk (bilateral CVA), funding risk (FVA) of self-default potential hedging (LVA), collateral (CollVA) and market hedging positions (HVA), as well as tail risk (KVA). These pricing metrics create a framework in which we can comprehensively value trading activity. An immediate consequence of this is the emergence of a potential difference between fair value accounting and internal accounting. This piece of work also explains the difference between both of them, and how to perform calculations in both worlds in a realistic and coherent manner, demonstrating via arbitrage-impossibility arguments that an XVA frameworks should be used in both cases.

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