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Scenario-based stochastic model predictive control for dynamic option hedging

Bemporad, Alberto and Gabbriellini, Tommaso and Puglia, Laura and Bellucci, Leonardo Scenario-based stochastic model predictive control for dynamic option hedging. In: Decision and Control Conference. IEEE, Hilton Atlanta Hotel, Atlanta, December 15-17, 2010, 6089 -6094. ISBN 978-1-4244-7745-6 (2010)

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For a rather broad class of financial options, this paper proposes a stochastic model predictive control (SMPC) approach for dynamically hedging a portfolio of underlying assets. By employing an option pricing engine to estimate future realizations of option prices on a finite set of one-step-ahead scenarios, the resulting stochastic optimization problem is easily solved as a least-squares problem at each trading date with as many variables as the number of traded assets and as many constraints as the number of predicted scenarios. After formulating the dynamic hedging problem as a stochastic control problem, we test its ability to replicate the payoff at expiration date for plain vanilla and exotic options. We show not only that relatively small hedging errors are obtained in spite of price realizations, but also that the approach is robust with respect to market modeling errors.

Item Type: Book Section
Identification Number: 10.1109/CDC.2010.5717004
Uncontrolled Keywords: SMPC; dynamic option hedging; least squares problem; option pricing engine; scenario-based stochastic model predictive control; stochastic optimization problem; financial management; least squares approximations; optimisation;predictive control; pricing; stochastic systems
Subjects: H Social Sciences > HB Economic Theory
Q Science > QA Mathematics
T Technology > TJ Mechanical engineering and machinery
Research Area: Computer Science and Applications
Depositing User: Professor Alberto Bemporad
Date Deposited: 29 Jul 2011 10:52
Last Modified: 04 Aug 2011 07:29
URI: http://eprints.imtlucca.it/id/eprint/739

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