Historical Scenarios with Fully Flexible Probabilities

Abstract

After reviewing the parametric and scenario-based approaches to risk management, we discuss a methodology to enhance the flexibility of the scenario-based approach. We change the probability of each scenario, and then we compute the ensuing p&l distribution and all relevant statistics such as VaR and volatility. The probabilities can be changed to reflect specific market conditions, advanced estimation techniques, or partial information, using the entropy-based Fully Flexible Views technique. The implementation of this approach is trivial, as no costly repricing is needed. Commented code is available at symmys.com.

Keywords: Exponential Smoothing, Kernel Smoothing, Parametric VaR, Monte Carlo Simulations, Stress-Test, Fully Flexible Views, Entropy Pooling, Multivariate Histogram, Empirical Distribution, Dirac Delta, Kullback-Leibler Divergence

JEL Classification: C1, G11