# Disentangling Price, Risk and Model Risk: V&R measures

## TL;DR

This paper introduces a novel framework for assessing intrinsic risk in financial positions by evaluating model and price uncertainties through a family of probability measures and derivative-based testing.

## Contribution

It develops a new interpretation of quasiconvex duality in a Knightian setting and constructs Value&Risk measures based on derivative testing of pricing models.

## Key findings

- New interpretation of quasiconvex duality in a Knightian context
- Construction of Value&Risk measures using derivative testing
- Framework for assessing additional capital needed for acceptability

## Abstract

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\&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 \textquotedblleft test\textquotedblright\ the pricing measures. We further introduce and study a general class of Value\&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 $X$.