Exposure & CVA for Large Portfolios of Vanilla Swaps : The Thin-Out Optimization

In this article we present an efficient optimization for calculating the exposure and CVA for large portfolios of vanilla swaps. It is based on a "thin-out" procedure applied to fixed payment streams, which reduces a very frequent stream of payments to a much less frequent one. The procedure requires careful handling of the path-dependence that arises from the floating legs of the swaps. We compute the exposure and CVA for a large portfolio of fixed-for-floating swaps, and find that our approximation reduces the computation time for the portfolio to that of a single swap, with a roughly annual schedule. Moreover, the approximation maintains a particularly high accuracy. Our technique is entirely model independent and can be applied to various instruments such as FX-forwards, cross-currency swaps etc