Efficient PDE based numerical estimation of credit and liquidity risk measures for realistic derivative portfolios

In the Basel III accords in 2013, it was stated that financial institutions should charge Credit Value Adjustment (CVA) to their counterparties for (previously under-regulated) Over-The-Counter (OTC) trades. This CVA can be used to hedge a possible default of the counterparty. One important ingredient of CVA is the calculation of the future exposure of the portfolio on which CVA has been charged. This future exposure is also used to determine more recent value adjustments like Debt Value Adjustment (DVA) and Capital Value Adjustments (KVA), and can be calculated from a future distribution of the portfolio value. This distribution can also be used to compute quantiles which are so-called “worst case” scenarios, and are therefore relevant for risk management. Computing the distribution of future portfolio values requires simulating the future states of the risk factors, and then evaluating the portfolio in all these future states. As the number of risk drivers in a typically traded portfolio is high, computing exposure for portfolios is a numerical challenge. In this thesis we look into multiple numerical techniques for the computation of exposures of realistic derivative portfolios. One of the key contributions of this thesis is the Finite Difference Monte Carlo (FDMC) method for an efficient computation of future exposure.