Abstract
Under the assumption of market completeness, the traditional Black-Scholes-Merton theory establishes the relationship between non-arbitrage and risk neutrality in the underlying asset and its derivatives. By constructing the hedging portfolio, the risk of derivatives can be diminished. However, the real-world market is incomplete. It is impossible to hedge perfectly, but this also makes statistical arbitrage possible. Statistical arbitrage does not guarantee profit from each trade, but it makes possible profit “on the average” after repeating similar trade strategies several times. In this research, we try to build several “model free” hedging strategies, such as Delta, stop-loss and adjusted stop-loss, and stochastic volatility “model free” hedging strategies, such as Delta-Gamma and corrected Delta, for index options. We test these strategies with data from the U.S. and Taiwan. Under several scenarios, e.g., different times to maturity, moneyness, future trends, we investigate (1) the performance of these hedging strategies and (2) the opportunity of statistical arbitrage. The empirical results in American call show that preceding strategies bring the opportunity of statistical arbitrage in substance. Delta hedging strategy is more stable but brings fewer profits on the average. On the other hand, stop-loss hedging strategy brings more profits on the average but is less stable. Adjusted stop-loss hedging strategy brings higher average return under the up trends.