AUTOMATED OPTION PRICING: NUMERICAL METHODS

Pierre Henry-Labordère ()
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Pierre Henry-Labordère: Société Générale, Global Markets, Quantitative Research, 17 cours Valmy, La Défense, France

International Journal of Theoretical and Applied Finance (IJTAF), 2013, vol. 16, issue 08, 1-27

Abstract: In this paper, we investigate model-independent bounds for option prices given a set of market instruments. This super-replication problem can be written as a semi-infinite linear programing 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: Linear programing; model-independent bounds; weighted Monte Carlo (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (3)

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DOI: 10.1142/S0219024913500428

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