流動性對於GARCH選擇權評價的影響

Liquidity on GARCH Option Pricing

鄭開明(Kai-Ming Cheng)

指導教授 ： 蘇永成

共同指導教授 ： 王耀輝(Yaw-Huei Wang)

國立臺灣大學/管理學院/財務金融學研究所/碩士(2008年)

https://doi.org/10.6342/NTU.2008.01231

摘要

許多實證的研究都顯示Black-Scholes的選擇權定價模型會因為一些不正確的假設而存有系統性的誤差. 在實際上的應用來說, Black-Scholes的隱含波動性會隨著選擇權的價內和價外(moneyness)和距離到期日時間長短而改變. 為了解決這個問題, 許多研究學者都努力研發出新的選擇權定價模型. 在這份論文裡, 探討的是Heston和Nandi的GARCH模型對於AMEX選擇權市場的定價有效度. 這份論文一共採樣了十二家公司並依照它們的流動性(由交易量來代表), 資本額, 和本益比來加以區分. 然後, 依照不同的分類, 對這些公司進行MLE的分析. 雖然HN GARCH整體來說的估計比較準確, 它特別不適合對於那些資本額比較小的公司進行選擇權定價, 而且它對於低本益比的公司也會有比較明顯的選擇權價錢低估. 不過, 對於那些流動性比較差的公司, 也就是說它們的選擇權其實實質上比較像是歐式選擇權的那些公司, 它的估計就相當值得參考.

關鍵字

Black-Scholes選擇權定價模型 ； HN GARCH模型 ； AMEX選擇權市場 ； MLE分析 ； 流動性

並列摘要

Many empirical researches have indicated that the Black-Scholes option pricing model demonstrate systematic biases due to some unreasonable assumptions. In practice, Black-Scholes implied volatilities tend to vary depending on moneyness and time to maturities. In response to this problem, many researchers have devoted themselves to creating new option pricing models. In this paper, the pricing efficiency of Heston and Nandi GARCH (HN GARCH) model is examined on the AMEX option market. A total of twelve companies are sampled and classified by liquidity (trade volume), market capitalization, and P/E ratio. Analyses are then carried out using the MLE method on different categories of companies. It is found that, while HN GARCH model has smaller valuation errors overall, they appear to be ill-suited for valuation of small market capitalization companies and display notable underpricing for options of low P/E ratio companies. They do, however, do a good job modeling the option prices of lower liquidity companies, whose options are much more European in practice.

並列關鍵字

Black-Scholes option pricing model ； HN GARCH model ； AMEX option market ； MLE method ； Liquidity

參考文獻

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