Encyclopedia of Financial Models II

Managing the Model Risk with the Methods of the Probabilistic Decision Theory

VACSLAV S. GLUKHOV, PhD

Head of Quantitative Strategies and Data Analytics, Liquidnet Europe Ltd, London, United Kingdom

Abstract: Practical applications of financial models require a proper assessment of the model risk due to uncertainty of the model parameters. Methods of the probabilistic decision theory achieve this objective. Probabilistic decision making starts from the Bayesian inference process, which supplies the posterior distribution of parameters. Bayesian incorporation of priors, or opinions, which influence posterior confidence intervals for the model parameters, is indispensable in real-world financial applications. Then, the utility function is used to evaluate practical implications of uncertainty of parameters by comparing the relative expected values of differing decisions. Probabilistic decision making involves computer simulations in all realistic situations. Still, a complete analytical treatment is possible in simple cases.

Practical applications of financial models require their parameters to be given concrete numerical values. These values are typically fitted to empirical data to ensure that the model predictions match historical observations. Parameter values obtained by such fitting procedures never propagate into the future unchanged: Tracing the model’s steps back in time, we find that its parameters are always more or less in error. The convention is that predictions ...