The influence of skewness and kurtosis on the determination of value at risk for TAIEX futures and options

[[abstract]]本研究主要是探討偏態與峰態對於風險值衡量的影響，所估計的風險性資產為台指期貨與台指買權。我們解除對於標的資產常態分配的假設，使用Cornish-Fisher展開式來修正分配，並使用delta-gamma的二階泰勒展開來計算選擇權的風險值。另外，在選擇權風險值的計算模型設計上，加入其他影響的因子，包括vega、theta，期望能夠改善估計的結果。 為了比較考慮報酬率分配的偏態與峰態是否會影響風險值估計的準確度，我們以不考慮偏態與峰態的二階模型、考慮偏態的三階模型以及同時考慮偏態與峰態的四階模型來計算風險值，波動度則以移動平均法及指數加權移動平均法做估計，另外再加上歷史模擬法做比較。在樣本的選擇上，期貨採用近月契約，選擇權則採用價平買權，並以台指期貨做為台指選擇權之標的資產。實證結果發現，由於偏態與峰態具有顯著相關性，因此單獨考慮偏態的結果比不考慮差，但同時考慮偏態與峰態則可改善績效，是估計表現最佳的模型。[[abstract]]This study analyses the influence of skewness and kurtosis on VaR. The risky assets are TAIEX and Options. We loose the assumption of normal distribution for the underlying assets and then use Cornish-Fisher expansion to determine the distribution of risk factors. On the other side, we used second order Taylor expansion to estimate the VaR of options. Moreover, we add factors of vega and theta for VaR model of options. We used three models to estimate VaR. The model considers the first two moments only, which neglect the skewness and kurtosis, the model considers the first three moments which adds the skewness, and the model consider the first four moments, which also adds the kurtosis. Volatilities are estimated by moving average (MA) and exponential weight moving average (EWMA). We also compared these results with historical simulation method. We determined the VaRs of the closest delivery month futures contract and near-the-money calls. We found the model considering first four moments performs best. Considering skewness but neglecting kurtosis will not increase the accuracy of VaR determination. This may be because the skewness and kurtosis are highly correlated