Gram-Charlier GARCH選擇權演算法的評價與避險績效

Abstract

本文以Gram-Charlier GARCH選擇權演算法配適於臺指選擇權的市場資料，並與BS公式解相比較，藉以瞭解GARCH選擇權演算法納入高階動差資訊後的評價與避險績效。市場資料顯示臺股指數報酬率的分配具有異質波動性，而且顯著不服從常態分配，因此BS模型會錯估臺指選擇權的價格；Gram-Charlier GARCH選擇權演算法考慮臺股指數的異質波動性、波動不對稱性與報酬率分配的高階動差值，評價績效顯著較佳。但是Gram-Charlier GARCH 選擇權演算法仍有明顯的評價誤差，臺股指數的日內波動性以及選擇權市場的流動性可以顯著解釋評價誤差。此結果反應出GARCH模型對於刻劃股價指數波動性的過程仍有不足，有必要進一步考慮跳躍風險溢酬或流動性效應的影響。避險績效測試結果顯示BS模型優於Gram-Charlier GARCH選擇權演算法，這可能是因為高階動差的敏感變動降低了避險參數估計的準確性，導致GARCH選擇權演算法呈現較差的避險績效。

The article applies Gram-Charlier GARCH option pricing algorithm to TAIEX options, in order to investigate the performance of the option pricing algorithm which considers the higher moments of underlying asset returns. We find that both GARCH algorithm and BS model systematically mis-price the TAIEX options. The GARCH algorithm performs better than BS model, but the pricing error of GARCH algorithm is still significant. A regression analysis shows that the explanatory factors for the pricing error of GARCH algorithm include intraday volatility of underlying index, and also the liquidity of the option markets. This implies that the GARCH algorithm with higher moments included still cannot totally capture the rapidly changing distributions of the underlying index returns, but an integrated approach incorporating jumps in return or volatility and the liquidity effect may be promising. Finally, the hedging simulation demonstrates that the Gram-Charlier GARCH algorithm is disappointing. The reason behind its poor performance may be the high variation of the daily estimate of the skewness parameter decreases the accuracy of delta estimation.