Automated Option Pricing: Numerical Methods

23 Pages Posted: 5 Dec 2011

Date Written: December 5, 2011

Abstract

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.

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, C60

Suggested Citation

Henry-Labordere, Pierre, Automated Option Pricing: Numerical Methods (December 5, 2011). Available at SSRN: https://ssrn.com/abstract=1968344 or http://dx.doi.org/10.2139/ssrn.1968344

Pierre Henry-Labordere (Contact Author)

Qube Research & Technologies ( email )

Paris
France

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