변동성 조소를 이용한 이산적 헤지에 대한수리분석과 시뮬레이션

Empirical tests of option pricing models are often based on their comparative hedging performance in discrete time, with daily hedge portfolio rebalancing typically chosen as the desired discrete time interval. The analysis in this paper suggests that such tests encounter much difficulty in distinguishing between correctly specified and incorrectly specified models. To show this, we compare the hedging performance of a stochastic volatility model to that of a “naive” volatility smile method in a simulated market environment in the stochastic volatility model is correctly specified. Using algebraic analysis and simulation experiments, we compare discrete hedging performance calibrated from a volatility skew with that from a stochastic volatility model consistent with the true underlying stochastic process. We find that a well specified stochastic volatility model offers little improvement over an ad-hoc volatility skew calibration. This helps at least partially explain why volatility skews are widely used by options professionals. These results also have implications for empirical tests of option pricing models.