GARCH選擇權訂價模型:那斯達克100追蹤股票之實證結果

Abstract

這篇論文探討Heston與Nandi所共同提出的GARCH選擇權訂價模型，並以那斯達克100追蹤股票為標的比較此GARCH模型相對於Black-Scholes之表現。GARCH參數採用兩種估計方法：（1）最大概似估計法，（2）非線性最小平方法。實證結果發現非線性最小平方法表現明顯較好，特別是它能解釋價外選擇權的波動率的微笑曲線，我們將GARCH模型的優異訂價表現歸因於該模型能同時捕捉標的資產歷史價格的過去資訊及選擇權價格所隱含之未來資訊。

This thesis investigates the empirical performance of Heston-Nandi GARCH option pricing model relative to an ad hoc Black-Scholes model using QQQ call option data. The GARCH model is examined from two perspectives: (1) maximum likelihood estimation, and (2) non-linear least square estimation. We find that the GARCH model with parameters estimated by non-linear least squares does better across all moneyness (K/S) categories, even though the ad hoc Black-Schole model updates the implied volatility by option prices. In particular, it can explain a significant part of volatility smile in out-of-money options. The improvement is largely due to the ability of the GARCH model to simultaneously capture the information of historical index series and current option prices.