Testing the Martingale Hypothesis in a Risk-Neutral Economic Scenarios Generator

This paper examines how statistical tests for martingale hypothesis can be applied to au- dit a risk-neutral Economic Scenarios Generator (ESG). The martingale test usually used to appreciate the risk-neutrality of the generated scenarios consists in testing that the mean of discounted asset prices is constant over time, which is a necessary condition for a martingale process. Although we have not found many studies that refer to statistical martingale tests in the framework of ESG, we have noticed that this approach can be very useful from the point of view of the actuarial function, allowing for example to detect implementation errors in the ESG and provide results more easily interpretable in sensitivity analysis than the standard mar- tingale test. Nevertheless, their application can raise many questions for the actuarial function, especially as concerns the choice of the tests retained, the ESG variable (asset) to which we apply the test and the acceptance threshold, and we will thus propose some recommendations for the use of these tests within a risk neutral ESG.