Automated Option Pricing: Numerical Methods
Société Générale - Paris, France
December 5, 2011
In this paper, we investigate model-independent bounds for option prices given market instruments.This super-replication problem can be written as a semi-infinite linear programming problem. As these super-replication prices can be large and the densities Q which achieve the upper bounds quite singular, we restrict Q to be close in the entropy sense to a prior probability measure at a next stage. This leads to our risk-neutral Weighted Monte-Carlo approach which is connected to a constrained convex problem. We explain how to solve efficiently these large-scale problems using a primal-dual interior-point algorithm within the cutting-plane method and a quasi-Newton algorithm. Various examples illustrate the efficiency of these algorithms and the large range of applicability.
Number of Pages in PDF File: 23
Keywords: sub/super-replication, model-independent bounds, semi-infinite linear programming, duality, primal-dual interior-point, cutting-plane, risk-neutral weighted Monte-Carlo
JEL Classification: C00, C60working papers series
Date posted: December 5, 2011
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