# Dynamic option hedging via stochastic model predictive control based on scenario simulation

*Alberto Bemporad*,
*Leonardo Bellucci* and
*Tommaso Gabbriellini*

*Quantitative Finance*, 2014, vol. 14, issue 10, 1739-1751

**Abstract:**
Derivative contracts require the replication of the product by means of a dynamic portfolio composed of simpler, more liquid securities. For a broad class of options encountered in financial engineering we propose a solution to the problem of finding a hedging portfolio using a discrete-time stochastic model predictive control and receding horizon optimization. By employing existing option pricing engines for estimating future option prices (possibly in an approximate way, to increase computation speed), in the absence of transaction costs the resulting stochastic optimization problem is easily solved at each trading date as a least-squares problem with as many variables as the number of traded assets and as many constraints as the number of predicted scenarios. As shown through numerical examples, the approach is particularly useful and numerically viable for exotic options where closed-form results are not available, as well as relatively long expiration dates where tree-based stochastic approaches are excessively complex.

**Date:** 2014

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