In this paper, we use copulas to define multivariate risk - neutral distributions. We can then derive general pricing formulas for multi - asset options and best possible bounds with given volatility smiles. Finally, we then apply the copula framework to define 'forward-looking' indicators of...

In this paper, we consider the open question on Spearman's rho and Kendall's tau of Nelsen [1991]. Using a technical hypothesis, we can answer in the positive. One question remains open: how can we understand the technical hypothesis? Because this hypothesis is not right in general, we could...

In this paper, we consider the problem of bounds for distribution convolutions and we present some applications to risk management. We show that the upper Frechet bound is not always the more risky dependence structure. It is in contradiction with the belief in finance that maximal risk...

In this paper, we study the approximation procedures introduced by Li, Mikusinski, Sherwood and Taylor [1997]. We show that there exists a bijection between the set of the discretized copulas and the set of the doubly stochastic matrices. For the Bernstein and checkerboard approximations, we...

Strategies are often analyzed without confronting quantitatively the clients' views. They also may present an overfitting problem which is detrimental to the investor and the client. In this paper, we present a new quantitative framework that enables the clients and investors alike to test their...

This paper is concerned with the relation between spot and implied volatilities. The main result is the derivation of a new equation which gives the dynamics of the spot volatility in terms of the shape and the dynamics of the implied volatility surface. This equation is a consequence of...