Monte Carlo Calculation of Exposure Profiles and Greeks for Bermudan and Barrier Options under the Heston Hull-White Model

TL;DR

This paper introduces an efficient Monte Carlo method using the Stochastic Grid Bundling Method to evaluate exposure profiles and Greeks for Bermudan and barrier options under complex Heston-Hull-White models, aiding CVA calculations.

Contribution

It presents a novel backward dynamics framework and an adaptive Monte Carlo approach for pricing and risk assessment of complex options under stochastic volatility and interest rate models.

Findings

Efficient computation of exposure profiles and Greeks using SGBM.

Application to Bermudan and barrier options under Heston-Hull-White models.

Facilitates CVA calculation with minimal additional effort.

Abstract

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.