Model01: Quantifying the Risk of Incremental Model Changes

DV01, the dollar value impact of a 1 basis point change in a yield curve is one of the most basic and widely used measures of market risk. Similar quantities and sensitivities have been defined for other parameters or “risk drivers” for a given, fixed model. In this present work we provide a meaningful and intuitive notion of Model01, which attempts to capture the analogue of a “1 basis point” bump in the space of models, beyond simple parametric changes. Importantly, our technique successfully calibrates each of these bumped models to the same set of liquid reference contracts. This turns out to be fundamental for a proper assessment of Model01 among exotic portfolios, and allows a meaningful comparison of the Model01 dollar value against the total reference price of a portfolio. Using the same procedure, it is possible to compute Model01 for single trades or portfolios of multiple trades, across different asset types and underliers, due to the flexibility of Weighted Monte Carlo techniques, on which it relies. The literature on quantification of model risk is limited. We will highlight the main features of R. Cont on model uncertainty and P. Glasserman and X. Xu on model risk, and compare Model01 against these approaches. The contributions from the present effort are manifold. We put forward the Hellinger distance as a more intuitive and genuine metric in the space of probability distributions, in contrast with relative entropy, which is more commonly used in the financial literature. We highlight connections between Model01 and an active area of research called information-geometry. This field applies the methods of differential geometry to the problem of statistical inference, and in particular, the problem of defining intuitive notions of distances across probability distributions. The problem at hand is strongly related, with a meaningful quantification of model uncertainty calling for a normalized measure of distances in the space of models. A fruitful connection and further explorations of these ideas should come then as no surprise. We motivate an interpretation of relative entropy as a distance squared. We employ this to analyze P. Glasserman and X. Xu techniques and cast them in rescaled units, revealing a linear dependence of their risk profiles which can be explained and proved. To the authors' best knowledge, these contributions represent novel undertakings in the financial literature, with the Hellinger distance, the interpretation of relative entropy and the introduction of information-geometry techniques being put forward in the context of model sensitivity for the first time in this present work. We apply the techniques of information geometry to shed light into relative entropy and the Hellinger distance, and reveal a natural Riemannian geometric structure in the parameter space of the alternative, bumped models used to compute Model01. The application of these concepts further enriches the interpretation of our results. Armed with these techniques, we demonstrate that Model01 intrinsically depends on the effective marginal covariance between a set of liquid instruments used for model calibration, and a portfolio of more exotic products. As the level of “exoticity'' or illiquidity of this portfolio increases, so does Model01. Model01 represents a flexible tool, potentially applicable to a wide variety of financial instruments, providing a glimpse into portfolios' model sensitivity, in a unified way.