| dc.description.abstract | In this thesis we consider two alternatives to the Brute Force approach for credit value adjustment (CVA) calculations for interest rate swaps. Both methods, the \textit{Proxy approach} as well as the \textit{CVA Notional} apply a regression-approximation for the portfolio value by using the least squares Monte-Carlo algorithm. We see how the performance of the Proxy approach is dependent on the approximation's ability to give a satisfying representation of the portfolio value in the entire state space, while the CVA notional represents an improvement as it is less sensitive to the proxy quality. This is achieved by a rewriting of the CVA expression, which also leads to a beneficial decoupling of the portfolio value and the cash flows generated by the portfolio contracts. By only relying on the regression proxy to denote whether the portfolio is positive or negative, and subsequently valuing the potential loss (given counterparty default and a positive portfolio value) by using simulated cash flows, the CVA notional yields more precise calculations. The difference is particularly prominent when considering non-linear portfolios. By being less dependent on the proxy, one can use fewer basis functions and less simulations in the regression and still calculate the CVA precisely when compared to the brute force benchmark.
Furthermore we demonstrate the benefits of a four-factor Cheyette model in governing the dynamics of interest rate derivatives. We see how the four stochastic factors yields a desirable flexibility in replicating the nature of the modelled yield curve, and how its Markov properties makes it a suitable choice as it reduces computational effort in a simulation framework. | |
