Bayesian Risk Management

Matt Sekerke’s thesis in Bayesian Risk Management: A Guide to Model Risk and Sequential Learning in Financial Markets (Wiley, 2015) is important and, even if not unassailable (just ask all the frequentists), readily defensible:

[T]he greatest obstacle to the progress of quantitative risk management is the assumption of time-invariance that underlies the naïve application of statistical and financial models to financial market data. A corollary of this hypothesis is that extreme observations seen in risk models are not extraordinarily unlucky realizations drawn from the extreme tail of an unconditional distribution describing the universe of possible outcomes. Instead, extreme observations are manifestations of inflexible risk models that have failed to adapt to shifts in the market data. The quest for models that are true for all time and for all eventualities actually frustrates the goal of anticipating the range of likely adverse outcomes within practical forecasting horizons. (pp. 4-5)

 

Sekerke wants to replace the normally overly complex risk model of classical statistics with a set of models, which are evaluated on their ability to generate useful predictions and which are penalized for complexity. “Though common practice routinely works exclusively with a single model, Bayes factors will always be computable for the chosen model relative to any conceivable alternative specification, so long as informative priors are used. … If one is seriously interested in knowing when models are in danger of breaking down—or equivalently, when the dynamics of markets are undergoing a significant change relative to recent history—the information contained in the Bayes factor is crucially important.” (p. 50)

Bayesian methods are superior to classical methods in numerous ways. One notable difference is that Bayesian inference not only captures the distinction between risk (measurable randomness) and uncertainty (which recognizes that randomness cannot be definitively measured) but “makes visible and quantifiable one element of generalized risk that has been deemed inaccessible to analysis. In fact, the possibility of making model comparisons between models with different discount factors makes it possible to speak of the degree of uncertainty in a meaningful way.” (p. 84)

Sekerke’s Bayesian Risk Management is written for quants, with the appropriate amount of math, but even non-quants can learn something from it. In nine chapters it covers models for discontinuous markets; prior knowledge, parameter uncertainty, and estimation; model uncertainty; introduction to sequential modeling; Bayesian inference in state-space time series models; sequential Monte Carlo inference; volatility modeling; asset-pricing models and hedging; and from risk measurement to risk management.