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We introduce a new method to calculate the credit exposure of Bermudan,discretely monitored barrier and European options. Core of the approach is theapplication of the dynamic Chebyshev method of Glau et al. (2019). The dynamicChebyshev method delivers a closed form approximation of the option pricesalong the paths together with the options' delta and gamma. Key advantage isthe polynomial structure of the approximation, which allows us a highlyefficient evaluation of the credit exposures, even for a large number ofsimulated paths. The approach is highly flexible in the model choice, payoffprofiles and asset classes. We compute the exposure profiles for Bermudan andbarrier options in three different equity models and compare them to theprofiles of European options. The analysis reveals potential shortcomings ofcommon simplifications in the exposure calculation. The proposed method issufficiently simple and efficient to avoid such risk-bearing simplifications.

Fast Calculation of Credit Exposures for Barrier and Bermudan options using Chebyshev interpolation