Automated Option Pricing: Numerical Methods

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.

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, C60

working papers series