Algorithmic Counterparty Credit Exposure For Multi-Asset Bermudan Options

For an efficient computation of the counterparty credit exposure profiles of the multi-asset options, a simulation-based method, named the Stochastic Grid Bundling Method (SGBM), is applied. The method is based on a 'regression later' technique used for the conditional expectation approximation and a bundling (or 'binning') technique used for state space partitioning. In the case of high-dimensional underlying asset processes, by using the bundling technique, the accuracy of exposure profiles is improved significantly, and the computation speed is reasonably fast. A detailed analysis for the bundling technique and regression approximation technique used in SGBM is given via various numerical examples. We provide an efficiency comparison of SGBM, the Standard Regression Method (SRM), and the Standard Regression Bundling Method (SRBM). We also show that for discontinuous payoffs, such as digital options, by using the bundling technique appropriately, SGBM can get accurate and stable results of option prices and exposure profiles. Compared with the benchmark results of one-dimensional European and Bermudan options, the SGBM has high accuracy in the computation of exposure profiles. The efficient calculation of the expected exposure (EE) by using SGBM forms the basis of the credit value adjustment (CVA) for multi-asset portfolios.