This paper aims to unify exotic option closed formulas by generalizing a large class of existing formulas and by setting a framework that allows for further generalizations. The formula presented covers options from the plain vanilla to most, if not all, mountain range exotic options and is...

The Black-Scholesmodelis basedona one-parameter pricingkernel with constantelasticity. Theoretical and empirical results suggest declining elasticity and, hence, a pricing kernel withat leasttwo parameters.We price European-style optionson assets whose probability distributions have two unknown...

We consider two sequences of Markov chains inducing equivalent measures on the discrete path space. We establish conditions under which these two measures converge weakly to measures induced on the Wiener space by weak solutions of two SDEs, which are unique in the sense of probability law. We...

We review the relations between adjoints of stochastic control problems with the derivative of the value function, and the latter with the value function of a stopping problem. These results are applied to the pricing of contingent claims.

No front-office software can survive without providing derivatives of option prices with respect to underlying market or model parameters, the so called Greeks. If a closed form solution for an option exists, Greeks can be computed analytically and they are numerically stable. However, for...

In both complete and incomplete markets we consider the problem of fulfilling a financial obligation xc as well as possible at time T if the initial capital is not sufficient to hedge xc. This introduces a new risk into the market and our main aim is to minimize this shortfall risk by making use...