An Optimized Least Squares Monte Carlo Approach to Calculate Credit Exposures for Asian and Barrier Options
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Counterparty credit risk management has become an important issue for financial institutions since the Basel III framework was introduced. Expected exposure (EE) is defined as the average (positive) exposure at a future date, it is an essential component in the measurement of counterparty credit risk. This thesis aims to develop an efficient Monte Carlo method to calculate the expected exposures for Asian and barrier options. These options are path-dependent in that their payoffs depend on the historical prices of the underlying assets. Since analytical solutions are generally not available to path-dependent options, the evaluation of the expected exposures has to rely on numerical methods. Monte Carlo method is considered to be more efficient than other methods in particular for high dimension problems. We briefly introduce the concepts and terms regarding credit exposures in the Basel III framework. Then, we introduce Asian and barrier options as well as some basic pricing models. Next, we will extend the optimized least squares Monte Carlo (OLSM) method to calculate the credit exposures for Asian and barrier options and present our numerical results.