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Stochastic default intensity American XVA pricing: PDE model and computation
We derive a two-dimensional time-dependent PDE model for American derivatives’ pricing including the valuation adjustment (XVA), assuming mean-reverting default risk for the counterparty, and constant default risk for the self-party. There are two nonlinear source terms, one from the American constraint and one from the XVA, handled by a double-penalty iteration. Particular emphasis is placed on the accurate calculation of the free boundary for each value of the default intensity. We also derive asymptotic approximations to the XVA price and to the free boundary. We present numerical experiments to study the accuracy and effectiveness of the 2D PDE and asymptotic approximations.