Analyzing model robustness via distortion of the stochastic root: A Dirichlet prior approach

It is standard in quantitative risk management to model a random vector X of consecutive log-returns in order to ultimately analyze the probability law of the accumulated return. By the Markov regression representation, see [Rüschendorf, de Valk (1993)], any model for X can be decomposed into a vector U of i.i.d. random variables - accounting for the randomness in the model - and a multivariate function f - representing the economic reasoning behind. For most models, f is known explicitly and U may be interpreted as an exogenous risk factor affecting the return X. While existing literature addresses model uncertainty by manipulating the function f, we introduce a new philosophy by distorting the source of randomness U. We impose consistency conditions for a reasonable distortion and present a suitable probability law and a stochastic representation for U based on a Dirichlet prior. The resulting framework bears one distortion parameter c tuning the severity of the imposed distortion. The universal nature of the methodology is illustrated by means of a case study comparing popular models for X. As an inner-mathematical result, the consistency conditions of the suggested distortion function reveal interesting insights into the dependence structure between samples from a Dirichlet prior.     «

It is standard in quantitative risk management to model a random vector X of consecutive log-returns in order to ultimately analyze the probability law of the accumulated return. By the Markov regression representation, see [Rüschendorf, de Valk (1993)], any model for X can be decomposed into a vector U of i.i.d. random variables - accounting for the randomness in the model - and a multivariate function f - representing the economic reasoning behind. For most models, f is known explicitly and U...     »