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A stochastic model predictive control approach to dynamic option hedging with transaction costs

Bemporad, Alberto and Puglia, Laura and Gabbriellini, Tommaso A stochastic model predictive control approach to dynamic option hedging with transaction costs. In: Proceedings of the American Control Conference (ACC), 2011. IEEE, pp. 3862-3867. ISBN 978-1-4577-0080-4 (2011)

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This paper proposes a stochastic model predictive control (SMPC) approach to hedging derivative contracts (such as plain vanilla and exotic options) in the presence of transaction costs. The methodology is based on the minimization of a stochastic measures of the hedging error predicted for the next trading date. Three different measures are proposed to determine the optimal composition of the replicating portfolio. The first measure is a combination of variance and expected value of the hedging error, leading to a quadratic program (QP) to solve at each trading date; the second measure is the conditional value at risk (CVaR), a common index used in finance quantifying the average loss over a subset of worst-case realizations, leading to a linear programming (LP) formulation; the third approach is of min-max type and attempts at minimizing the largest possible hedging error, also leading to a (smaller scale) linear program. The hedging performance obtained by the three different measures is tested and compared in simulation on a European call and a barrier option.

Item Type: Book Section
Uncontrolled Keywords: Contracts, Europe, Measurement uncertainty, Minimization, Portfolios, Predictive models, Stochastic processes.
Subjects: H Social Sciences > HG Finance
Q Science > QA Mathematics
Research Area: Computer Science and Applications
Depositing User: Professor Alberto Bemporad
Date Deposited: 29 Jul 2011 11:00
Last Modified: 09 Jul 2012 09:42
URI: http://eprints.imtlucca.it/id/eprint/745

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