P.J. Meindl and J.A. Primbs (USA)
Dynamic hedging, transaction costs, control theory
We use receding horizon control to periodically hedge a short European call on an underlying asset under geometric Brownian motion and under stochastic volatility. The resulting absolute hedging errors are obtained via Monte Carlo simulation and compared to errors from delta hedging using both the Black Scholes model and Heston's stochastic volatility model. Our results show that receding horizon control's performance, even with extremely small lattices, is significantly superior, both statistically and economically, to delta hedging when reasonable transaction costs are included. Typical reductions in mean hedging error range from 10% to nearly 40% depending on the scenario.
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