![Sample our Mathematics & Statistics journals, sign in here to start your FREE access for 14 days]({"type":"image" , "src" : "/sda/5943/TOC-Subject-Sample-2021-Mathematics-Statistics.jpg"})
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.
Acknowledgements
The authors sincerely thank Alexandre Radicchi and Eric Remo Robert Reynolds for stimulating discussions. We also acknowledge MPS Capital Services for providing financial support for this research.
Notes
†The approach can easily be extended to other options as described by Bertsimas et al. (Citation2001), such as Asian options.
‡The results presented in this paper can immediately be extended to non-uniform trading intervals Δ T .
†In this particular case, the probability measure used for the asset price and portfolio dynamics coincides with the risk-neutral one. However, the reader should note that the approach of this paper relies on the real-world probability measure for the asset price and portfolio dynamics.