無模型隱含波動度及其資訊內涵─以外匯選擇權為例

Abstract

In this article, we follow Jiang and Tian (2005) to calculate the model-free implied volatility of foreign exchange options traded in the OTC market and the underlying assets are EUR/USD, GBP/USD and USD/JPY. In the first part, we calculate the model-free implied volatility and realized volatility constructed by intraday high-frequency data. In the second part, we compare the information content between model-free implied volatility, Black-Scholes (B-S) at-the-money implied volatility and historical volatility. The univariate regression results show that all of the three volatilities have significant predictability for future realized volatility, and the encompassing regression results show that the two implied volatilities contain more information than the historical volatility. Then, we compare the information between the model-free implied volatility and the B-S implied volatility. Although the results in Jiang and Tian (2005) suggest that the model-free implied volatility is a more efficient forecast for future realized volatility, our results get an overall conclusion that the model-free implied volatility does not predict future volatility better than the B-S implied volatility. We conjecture that there are only at most 9 quotes in the currency options market per day while there are much more quotes in equity option market per day. Since the model-free implied volatility is constructed from all of the market data, the limited available of market data leads to the result that it cannot have better predictability than the B-S implied volatility.