American Option Regular Hedge Based On Weighted Least Squares

This paper studies American option’s hedging. Delta is one of the important parameter for option’s hedging.The option’s hedging is an important topic in the theory and the practice of derivatives pricing, because in the real financial market, the risk management of derivative products has relation with hedging parameters. Alcock and Carmichael (1993) obtained an estimator of the American option price combining the canonical pricing method and the least square method. The results in this paper are derived from extending it. Compared with various methods available in the literature, this method is a non-parametric method and can reduce model risk which setting model brings. Besides, the method only needs the underlying assets’historical price data avoiding depending on the options’market price data.In this paper, simulation is carried out under the assumption of the Black-Scholes’ model and the Heston’s model. The data generated via Monte Carlo simulation are regard as the underlying assets’historical price. The delta of the American option can be obtained with the aid of MATLAB software. Then the effect of hedging can be compared. The results of simulation experiment show that the method in this paper is more suitable to the in-the-money option in the Black-Scholes’ model.But for the data generated by the Heston’s model, this method is obviously superior to the Black-Scholes’formula about Delta commonly used. So the canonical hedging is a method for model robustness.