無模型設定隱含波動度之誤差分析-以台股指數選擇權

Error analysis of Model-free Implied Volatility-use TXO

林旅仲(Lu-Chung Lin)

指導教授 ： 林允永 ； 李進生

淡江大學/商學院/財務金融學系碩士班/碩士(2008年)

https://doi.org/10.6846/TKU.2008.00834

摘要

有鑒於目前市場大都以Black-Scholes隱含波動度作為探討波動度的主要工具，而根據Jiang and Tian(2005)在服從跳躍擴散過程(jump-diffusion process)下所提出的無模型設定隱含波動度(model-free implied volatility)的觀念，進一步探討無模型設定隱含波動度與Black-Scholes隱含波動度在台灣指數選擇權上的波動度的差異，並且了解樣本內，兩種隱含波動度以Black-Scholes反推出的估計選擇權價格與真實選擇權價格的差異。另外比較樣本外與樣本內兩種模型有無變化。
實證結果可發現兩種隱含波動度相關性相當高，但是在誤差分析時可發現明顯差別。另外可發現不論樣本內或樣本外，Black-Scholes模型有較小的價格誤差，無模型設定隱含波動度有較大且不好的價格誤差，但在無模型設定隱含波動度在樣本外的估計選擇權價格誤差不完全比樣本內差，而Black-Scholes模型則有是有完全樣本外比樣本內差。

關鍵字

無模型設定隱含波動度 ； Black-Scholes模型

並列摘要

In recent years, Black-Scholes Implied Volatility has become the most famous tool in volatility researching. According to the idea of model-free implied volatility with jump-diffusion process that proposed by Jiang and Tian(2005), I prefer to know the difference between model-free and Black-Scholes Implied Volatility in TXO. More further, I compare in sample performance of two implied volatilities using Black-Scholes option pricing formula. Otherwise, I would like to know how pricing error going between in sample and out–of–sample.
Although empirical result shows these two implied volatilities has high correlation, there are distinct discrepancy in error test. No mater in or out-of-sample, Black-Scholes model has better performance in error test. In error test, in sample of model-free model is not exactly better than out-of-sample. But, in sample of Black-Sholes model is exactly better than out of sample.

並列關鍵字

Model-free Implied Volatility ； Black-Scholes model

參考文獻

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