Dynamic option hedging with transaction costs: A stochastic model predictive control approach. (6th September 2017)

• Record Type: Journal Article
• Authors: Graf Plessen, Mogens; Puglia, Laura; Gabbriellini, Tommaso; Bemporad, Alberto
• Other Names: Quevedo Daniel E. guestEditor.; Chatterjee Debasish guestEditor.
• Is Part Of: International journal of robust and nonlinear control. Volume 29:Number 15(2019)
• Page Start: 5058
• Page End: 5077
• Publication Date: 2017-09-06
• Subjects: financial options -- hedging techniques -- scenario generation -- stochastic model predictive control -- stochastic programming -- transaction costs; Automatic control -- Periodicals; Control theory -- Periodicals; Nonlinear systems -- Periodicals; 629.836
• DOI: 10.1002/rnc.3915
• Languages: English
• ISSNs: 1049-8923

Abstract

Summary: This paper proposes stochastic model predictive control as a tool for hedging derivative contracts (such as plain vanilla and exotic options) in the presence of transaction costs. The methodology combines stochastic scenario generation for the prediction of asset prices at the next rebalancing interval with the minimization of a stochastic measure of the predicted hedging error. We consider 3 different measures to minimize in order to optimally rebalance the replicating portfolio: a trade‐off between variance and expected value of hedging error, conditional value at risk, and the largest predicted hedging error. The resulting optimization problems require solving at each trading instant a quadratic program, a linear program, and a (smaller‐scale) linear program, respectively. These can be combined with 3 different scenario generation schemes: the lognormal stock model with parameters recursively identified from data, an identification method based on support vector regression, and a simpler scheme based on perturbation noise. The hedging performance obtained by the proposed stochastic model predictive control strategies is illustrated on real‐world data drawn from the NASDAQ‐100 composite, evaluated for a European call and a barrier option, and compared with delta hedging.