Counterparty Credit Risk and Credit Value Adjustment: A Continuing Challenge for Global Financial Markets, 2nd Edition

9.3 Monte Carlo Methodology

9.3.1 Simulation Model

The first task is to define the relevant risk factors and decide on the models to be used for their evolution. However, it is important to strike a balance between a realistic model and one which is parsimonious. For example, there are 50–60 or more risk factors defining an interest rate curve, whereas the simplest interest rate models involve only one factor. A model involving two or three factors may represent the right compromise. Such an approach will capture more of the possible curve movements than would a single-factor model, but without producing the unrealistic curve shapes and arbitrageable prices that a model for each individual risk factor might generate.

Another reason for simpler underlying models for risk factors is the need to incorporate co-dependencies (correlations)² in order to capture the correct multidimensional behaviour of the netting sets to be simulated. The correct description of the underlying risk factors and correlations leads to a significant number of model parameters. A balance is important when considering the modelling of a given set of risk factors (such as an interest rate curve) and the correlation between this and another set of risk factors (such as an interest rate curve in another currency). There is no point in having sophisticated univariate modelling and naïve multivariate modelling. Due to expertise in different product areas, an institution may have good univariate models for interest ...