流動性對於GARCH選擇權評價誤差的影響

Abstract

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。實際的應用方面， 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North American Industry Groups中30個不同產業的定價有效度。每個產業均取交易量最大與最小的標的公司進行研究。依照不同的產業分類，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，在流動性(交易量)較少或本益比特別高的公司也會出現比較大的評價誤差。

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 60 companies of 30 different industries in the North American Industry Groups. 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 trading volume companies and display notable pricing error for options of high P/E ratio companies. They do, however, do a good job modeling the option prices of higher liquidity companies.