不同波動度模型應用於台指選擇權評價之績效實證研究

Empirical Study of Performance by Different Volatility Model Applied to Evaluation of TAIEX Options

許江河(Philip Hsu) ； 林家民(Chia-Min Lin)

《國立虎尾科技大學學報》 30卷1期 (2011/03) Pp. 105-116

https://doi.org/10.6425/JNHUST.201103.0105

摘要

自Black & Sholes提出選擇權評價模式後，不但選擇權的評價問題受到廣泛的討論，也出現了許多不同的選擇權評價模型；儘管各模型都有其理論基礎，但在實務評價上往往都出現很大的誤差。本文嘗試透過七種波動度預測模型，對Black & Sholes模型進行修正，以找出這些修正的Black & Sholes模型何者評價誤差最小。這七種波動度預測模型分別爲歷史波動度模型、GARCH模型、指數平滑波動度模型和四種由交易人規則所計算的波動度模型。本文所採用的資料爲2002年1月至2009年11月的近月份台指選擇權日資料。實證結果發現，在所有模型中，經由交易人規則預測的波動度所修正的 Black & Sholes模型AHBS(下標 A3)對接近價平的選擇權的評價表現最佳，而深度價外的買權或賣權用原始的Black & Sholes模型評價的誤差最小。

關鍵字

選擇權評價 ； 波動度模型 ； 台指選擇權

並列摘要

After Black & Sholes proposed their famous option pricing model, the evaluation of options had been widely discussed and many different option pricing models were constructed. Although every model has its theoretical basis, most of them have the problem of huge errors of evaluation in their practice use. This paper attempts to modify the Black & Sholes model by using seven types of volatility forecasting model, and to find out the model which has the minimum error of evaluation. The seven volatility forecasting models are the historical volatility model, the GARCH model, the exponential smoothing model and four types of volatility forecasting model derived from trader's rules. The data used consists of the daily prices from the near month options, and spans from January 2002 to November 2009. Our findings suggest that the AHBS(subscript A3) model provides the minimum error of evaluation when the at-the-money options are evaluated and in respect of the out-of-money options the original Black & Sholes model seems to have the best performance.

並列關鍵字

Option valuation ； Volatility model ； TAIEX Options

參考文獻

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