封閉解GARCH選擇權評價模型於FTSE100選擇權市場之實證研究

Abstract

許多實證研究已經顯示Black-Scholes選擇權評價模型因不合理的假設而產生系統性的誤差。事實上，Black-Scholes的隱含波動度會因不同的履約價格與到期期限有由所不同。為了解決這個缺點，許多研究人員與學者已經開始致力於發展新的選擇權評價模型。此文章中，我們以FTSE100選擇權市場得資料測試了Heston和Nandi的HN GARCH模型的評價效率，並且以Dumas，Flemiming和Whaley的Ad Hoc Black-Scholes選擇權評價模型當作比較標的，藉以判斷HNGARCH模型是否有較好的評價效率。我們發現HN GARCH模型相較於Ad Hoc Black-Scholes無論是在in-sample或out-of-sample的實驗研究部分都有較小的評價誤差。

Many empirical researches have indicated that the Black-Scholes option pricing model demonstrates systematic biases due to some unreasonable assumptions. In practice, Black-Scholes implied volatilities tend to differ across exercise prices and time to maturities. For conquering the shortcoming, many researchers have devoted themselves to creating new option pricing model. In this article, we test the pricing efficiency of Heston and Nandi GARCH (HN GARCH) model in the FTSE 100 Index option market. As the benchmark model do we choose the Ad Hoc Black-Scholes model of Dumas, Flemming and Whaley (1998) which use a separate implied volatility for each option to fit to the smirk/smile in implied volatilities. We find that the HN GARCH has smaller valuation errors than ad hoc BS model both in-sample and out-of-sample.