無模型設定隱含波動率-S&P500指數期貨選擇權的隱含波動率之實證研究

Abstract

Britten-Jones and Neuberger (2000) derived the model-free implied volatility under the assumption that the price of underlying asset follows diffusion process. Jiang and Tian (2005) further introduce that the price of underlying asset follows jump-diffusion process using the above model-free implied volatility, and build a simple way to transfer the formula to a computing instrument using European option prices on the market. In the process of computing model-free implied volatility, we need to use the Black-Scholes model for the bridge of transferring implied volatility. However, there are many unreasonable assumptions in the Black-Scholes model, we use another bridge to transfer implied volatility in this paper for comparison. That is The Static Empirical Model introduced by Chen, Palmon and Wald (2003). They relax some unreasonable assumptions in the Black-Scholes model to derive The Static Empirical Model. The empirical study in this paper use the data of S&P 500 index futures options to compute the model-free implied volatility to test the efficiency in the option market. But we use the American option data in this paper. So we also use the method introduced by Barone-Adesi and Whaley (1987) to transfer the American option price to European option price to fit our model. At last, we find that when predicting the realized volatility in the future, the model-free implied volatility computed by the implied volatility transferred by The Static Empirical Model is more efficient than the implied volatility transferred by Black-Scholes model. And the prediction ability of model-free implied volatility from more option data is better than the implied volatility of one option (the implied volatility of Black-Scholes model and the implied volatility of The Static Empirical Model).