Model Risk for Market Risk Modeling

Standard risk management approaches fail to consider parameter uncertainty, which has led to improper risk management. Blind faith in parameter estimates has too often led to blind faith in the resulting VAR outputs, and when these estimates are too often exceeded the proposed solution is commonly to fatten up the tails by using exotic distributions. We show, however, that directly modeling the uncertainty in mean and variance returns using standard lognormal distributions can result in posterior distributions with high degrees of skewness and kurtosis. If we accept a simple world of time-varying expected returns and variances, the resulting uncertainty around these constantly shifting parameters places us squarely in this world of interesting and effective posterior distributions