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

Author

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  • Alberto Bemporad
  • Leonardo Bellucci
  • Tommaso Gabbriellini

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.

Suggested Citation

  • Alberto Bemporad & Leonardo Bellucci & Tommaso Gabbriellini, 2014. "Dynamic option hedging via stochastic model predictive control based on scenario simulation," Quantitative Finance, Taylor & Francis Journals, vol. 14(10), pages 1739-1751, October.
    • Handle: RePEc:taf:quantf:v:14:y:2014:i:10:p:1739-1751
    DOI: 10.1080/14697688.2011.649780
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    Cited by:

    1. Yuji Yamada & James A. Primbs, 2018. "Model Predictive Control for Optimal Pairs Trading Portfolio with Gross Exposure and Transaction Cost Constraints," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 25(1), pages 1-21, March.
    2. Peter Nystrup & Stephen Boyd & Erik Lindström & Henrik Madsen, 2019. "Multi-period portfolio selection with drawdown control," Annals of Operations Research, Springer, vol. 282(1), pages 245-271, November.

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