Disentangling price, risk and model risk: V&R measures

We propose a method to assess the intrinsic risk carried by a financial position X when the agent faces uncertainty about the pricing rule assigning its present value. Our approach is inspired by a new interpretation of the quasiconvex duality in a Knightian setting, where a family of probability measures replaces the single reference probability and is then applied to value financial positions. Diametrically, our construction of Value and Risk measures is based on the selection of a basket of claims to test the reliability of models. We compare a random payoff X with a given class of derivatives written on X, and use these derivatives to “test” the pricing measures. We further introduce and study a general class of Value and Risk measures \( R(p,X,\mathbb {P})\) that describes the additional capital that is required to make X acceptable under a probability \(\mathbb {P}\) and given the initial price p paid to acquire X.