Dynamic option hedging with transaction costs: A stochastic model predictive control approach
| Autor: | Laura Puglia, Mogens Graf Plessen, Tommaso Gabbriellini, Alberto Bemporad |
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| Rok vydání: | 2017 |
| Předmět: |
0209 industrial biotechnology
Mathematical optimization Optimization problem Linear programming Computer science Mechanical Engineering General Chemical Engineering Biomedical Engineering Exotic option Aerospace Engineering Barrier option 02 engineering and technology Industrial and Manufacturing Engineering Stochastic programming Expected shortfall 020901 industrial engineering & automation Computer Science::Computational Engineering Finance and Science Control and Systems Engineering Replicating portfolio 0202 electrical engineering electronic engineering information engineering 020201 artificial intelligence & image processing Quadratic programming Electrical and Electronic Engineering |
| Zdroj: | International Journal of Robust and Nonlinear Control. 29:5058-5077 |
| ISSN: | 1099-1239 1049-8923 |
| DOI: | 10.1002/rnc.3915 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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