| Summary: | 碩士 === 國立臺北大學 === 統計學系 === 98 === Options have been playing an important role in real financial market since the first option had traded. However, it is a major subject that how the rational price of options had been made. Black & Scholes (1973) set up the landmark of option pricing after they proposed the famous Black-Scholes option pricing model. In practice, one of the assumptions made in Black-Scholes (BS) option pricing model, namely volatility is a fixed constant, isn’t in accordance with the practices in real world. Scholars afterward try to release the assumption made by Black-Scholes and proposed so called stochastic volatility model which can categorized in discrete- and continuous-time model. Among discrete-time models, Duan (1995) introduced the model in quantitative economics, Generalized Autoregressive Conditional Heteroskedasticity (GARCH), to amend the assumption that volatility in Black-Scholes option pricing model is a fixed constant. Like most other option pricing models, the closed-form solutions do not exist. Heston & Nandi (2000) proposed a GARCH option pricing model with specific closed-form solution that can be directly derived by using numerical integration techniques. This research attempted to check out how the Heston & Nandi (2000) GARCH option pricing model perform in Taiwan Stock Exchange Capitalization Weighted Stock Index options (TXO) based on Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) and compared with BS option pricing model in option mispricing.
The results show that it is outperformed by BS option pricing model both in in-sample and out-of-sample valuation though Heston & Nandi (2000) released the assumption mentioned above. The significant mispricing could be caused by different data definitions. On the other hand, like Heston & Nandi (2000), the significant mispricing may also caused by the poor estimates of the parameters in the model.
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