Counterparty credit risk pricing and measurement of swaption portfolios

This paper introduces a technique for pricing and risk measurement of portfolios containing swaption contracts in the presence of counterparty credit risk, under general market model and volatility assumptions. An implementation of the radial basis function (RBF) method for solving Black-Scholes-type partial differential equations (PDEs) is proposed that takes advantage of the high degree of intercurve correlation present in term-structure models. The RBF-PDE technique is first used to price the swaptions in the absence of credit risk. As a by-product of this solution process, sets of RBF expansions for the value of each swaption at each time point are determined. These expansions, which can be evaluated in milliseconds, can then be incorporated into simulations for credit value adjustment and potential future exposure calculation. Several examples are shown that involve solving PDEs in as many as forty-eight spatial dimensions under both lognormal and local volatility.