Abstract Distortion functions are employed to define measures of risk. Receiver operating characteristic (ROC) curves are used to describe the performance of parametrized test families in testing a simple null hypothesis against a simple alternative. This paper provides a connection between...

We investigate a new method for pricing high-dimensional American options. The method is of finite difference type but is also related to Monte Carlo techniques in that it involves a representative sampling of the underlying variables. An approximating Markov chain is built using this sampling,...

We propose and test a new method for pricing American options in a high-dimensional setting. The method is centred around the approximation of the associated variational inequality on an irregular grid. We approximate the partial differential operator on this grid by appealing to the SDE...

In this paper we propose a general framework for quantification of model risk. This framework allows us to allocate regulatory capital to positions in a given market depending on the extent to which this market can be reliably modeled. Our approach is based on computing worst-case risk measures...

We propose a method for pricing high-dimensional American options on an irregular grid; the method involves using quadratic functions to approximate the local effect of the Black-Scholes operator. Once such an approximation is known, one can solve the pricing problem by time stepping in an...

In this paper we test several risk management models for computing expected shortfall for one-period hedge errors of hedged derivatives positions. Contrary to value-at-risk, expected shortfall cannot be tested using the standard binomial test, since we need information of the distribution in the...