Algorithmic Exposure and CVA for Exotic Derivatives

We develop the algorithmic approach for Counterparty exposure calculation and automate its application to arbitrary complicated instruments. Assuming that the portfolio is priced by the backward (American) Monte-Carlo method, our approach allows calculating the credit exposure as a pricing by-product, essentially without modifications in the usual pricing procedure.In particular, for the exposure calculation of callable instruments we manage to avoid a cumbersome aggregation of exercise indicators, applying them sequentially in parallel with the main pricing.We explain how the obtained exposure can be integrated into the Credit Valuation Adjustment (CVA), based on the extension of the pricing model with a Counterparty credit component.The presented approach to the exposure computation is formulated in an arbitrary probability measure. To perform the measure change we use the cross-currency model semantics and calibrate the model to the real-world measure using indexes projections