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Model-independent bounds for Asian options : a dynamic programming approach

We consider here the financial problem of pricing exotic options when there is uncertainty about the true underlying market model. Specifically, we study the problem of finding model-independent bounds on the price of an Asian option, when the call prices at the maturity date of the option are known. Our methods differ from most approaches to model independent pricing in that we consider the problem as a dynamic programming problem, where the controlled process is the conditional distribution of the asset at the maturity date. By formulating the problem in this manner, we are able to determine the model-independent price through a PDE formulation. Notably, this approach does not require specific constraints on the payoff- function (e.g. convexity), and would appear to be generalisable to many related problems. This is joint work with A.M.G. Cox.

CMAP UMR 7641 École Polytechnique CNRS, Route de Saclay, 91128 Palaiseau Cedex France, Tél: +33 1 69 33 46 23 Fax: +33 1 69 33 46 46