The Forecasting Quality of Implied Volatility─Evidence from Taiwan and U.S. Market

• Main Authors: Jyi-Tyng Shiue, 薛吉廷
• Other Authors: Huimin Chung
• Format: Others
• Language: zh-TW
• Published: 1999
• Online Access: http://ndltd.ncl.edu.tw/handle/19881806953447980077

碩士 === 淡江大學 === 財務金融學系 === 87 === Fleming(1998a) uses S&P100 index option to discuss whether implied volatility is an unbiased estimator of stock market volatility and whether the forecasting error of implied volatility and the market information set have orthogonal relationship. The empirical result indicates that implied volatility is a biased estimator , and it always produces higher estimation. Without the consideration that implied volatility is a biased estimator, using the linear model of implied volatility achieves a good result. The forecasting error of implied volatility and conditional volatility, including historical volatility model and GARCH(1,1) model, have orthogonal relationship. In other words, implied volatility model can''t explain the forecasting error of volatility, neither can historical model and GARCH(1,1) model. The purpose of this thesis is to explain why implied volatility is a biased estimator. A possible reason is that there is a bias and measuring error in option pricing model. Another possible reason is that option market is inefficient. Even if option market is efficient, the price of option may deviate from theoretical price because of the trading cost and incomplete factor from market. The issuing cost of securities and the inefficiency of option market might explain that the implied volatility in Taiwan warrant market is a biased estimator. Due to the measuring error of implied volatility deduced from Black-Scholes model, I adopt two-stage-least-square method to compare the ability of volatility forecasting and try to find out what is the best estimator of realized implied volatility. Furthermore, I also analyze the weekly and monthly data of S&P100 index option in order to understand the comparison result of each volatility model of U.S. option market. In Taiwan warrant market, the weekly empirical result indicates that implied volatility doesn''t have any information about volatility forecasting. The implied volatility of S&P100 index option performs better than that of covered warrant in Taiwan market. Although modified by two-stage-least-square method, the implied volatility in Taiwan and U.S. market is still a biased estimator. In Taiwan warrant market, however, using ARCH(5) or GARCH(1,1) volatility model can make a better prediction than using implied volatility model. When daily data is used to construct realized volatility, ARCH(5) will be a better volatility forecasting model for most of the sample data in Taiwan warrant market.