Hedge and Price American Options with Static Hedging Portfolio Method under Stochastic Volatility

Under stochastic volatility (SV), despite the abundant literature on American option pricing, there is little work on American option hedging. This paper develops a feasible and excellently performing static-hedging-portfolio (SHP) method for hedging and pricing an American option under SV, by constructing a portfolio of European options to match the payoff, delta, and vega of the target American option along its early exercise boundary. The novelty of the proposed SHP method is in incorporating the expected variance conditional on the stock price into Chung and Shih's (2009) method, and further improving their method by imposing the vega-matching condition. Our numerical analyses show the superiority of the proposed SHP method in effectively hedging and accurately pricing American options in the presence of SV, especially when the vega-matching condition is taken into account. For a large, randomly generated set of American option contracts, the average pricing error (hedging risk, measured by 5% Value at Risk) of the proposed SHP method ranges from 0.11% to 0.14% (0.78% to 0.88%) of the average option value, and the 5% Value at Risk of the proposed SHP method is around 3% that of the widely used dynamic delta-neutral hedging method.