Joining Risks and Rewards

Abstract

The dichotomy between risk analytics and pricing is well known amongst financial practitioners and researchers. For risk analysis, such as computing value at risk and credit exposures, expectations of future values must be computed under the real world measure. For pricing, expectations are computed under a risk neutral measure. This means that for calculations such as value at risk (VaR) and credit exposures (EEs, EPEs, etc) on derivative portfolios, risk factors are evolved to the horizon date under the real world measure, at which point the portfolio is repriced under a risk neutral measure.Simulation under the real world measure followed by repricing under a risk neutral measure is computationally intensive, especially when the repricing requires Monte Carlo. Because of the computational effort involved, shortcuts are often taken. One common shortcut is to assume the real world measure is the risk neutral measure, so that calculations can be done under one measure. This particular shortcut is especially problematic as it leads to results varying wildly depending on the numeraire chosen.Here we detail methods of avoiding this problem by combining the real world measure with the risk neutral measure. We present an application to risk analytics which speeds up the calculations by orders of magnitude, changing O(n^2) calculations to O(n) with a far smaller scaling constant. This allows the computation of exposures under the real world measure, obviating the need for the dangerous practice of computing exposures under a risk neutral measure.