  Valuation of Credit Valuation Adjustment (CVA) has become an important field
as its calculation is required in Basel III, issued in 2010, in the wake of the
credit crisis. Exposure, which is defined as the potential future loss of a
default event without any recovery, is one of the key elementsfor pricing CVA.
This paper provides a backward dynamics framework for assessing exposure
profiles of European, Bermudan and barrier options under the Heston and Heston
Hull-White asset dynamics. We discuss the potential of an efficient and
adaptive Monte Carlo approach, the Stochastic Grid Bundling Method}(SGBM),
which employs the techniques of simulation, regression and bundling. Greeks of
the exposure profiles can be calculated in the same backward iteration with
little extra effort. Assuming independence between default event and exposure
profiles, we give examples of calculating exposure, CVA and Greeks for Bermudan
and barrier options.
