The Method of the Optimal Volatility Estimator in TXO Under theBlack-Scholes Model

• Main Authors: Yi Wen Jeng, 鄭亦妏
• Other Authors: Yen-Sen Ni
• Format: Others
• Language: zh-TW
• Published: 2003
• Online Access: http://ndltd.ncl.edu.tw/handle/09886693390281467991

碩士 === 淡江大學 === 管理科學學系 === 91 === The underlying asset price, exercise price, risk-free interest rate, duration and volatility are the endogenous variables in the Black-Scholes option pricing model, and we can obtain the theoretical price of an option contract through the model. Five variables except the volatility variable could be collected form market or the option contract, but the volatility is hard to be defined. It can be sorted into two categories. One is counted by historical underlying asset price data, and the other is implied volatility (IV). The empirical results about the suitability between volatilities calculated by the Black-Scholes model and real volatilities the option contract faces are not identical. Some of empirical results in this study imply that IV model is the best estimator for calculating the volatility for TAIFEX stock index option (TXO), because it represents the true situation the option lies in. But other results show the opposite comments, i.e. IV are not the suitable estimator for pricing TXO, it will lead to estimating errors. The target of the study is a new product (TXO) in Taiwan, and this financial product is available since Dec.24, 2001. This research uses several methods for estimating the volatility for TXO, tries to find the optimal model to estimate the volatility, and search the causes of variation between theoretical value and market value for TXO. The findings are shown as follows. 1.To TXO, the volatilities estimated by the historical standard deviation and GARCH (1,1) model are the best estimators, and estimated by IV models are the worst. 2.Among the models of weighted implied volatility, the mis-pricing of the vega weighted implied volatility model is smallest. 3.The volatilities estimated by IV model are not optimal volatilities estimator, and it implies that the market is not mature. 4.The results are quit different between TXO and warrants: TXO call options are over-priced, and warrants are under-priced in Taiwan markets. We try to explain the differentiation by supply aspect, which is based on the demand-supply theory.