本文建構以一般化極端值分配(GEV)為基礎的選擇權評價模型，並探討極端事件發生(如次級房貸)後對報酬分配的偏態及峰態係數的影響。在實證上以距到期日不同到期期間的長短之臺指選擇權來評估次級房貸事件發生後的評價績效。結果發現GEV評價模型在極端事件後的評估績效明顯優於B-S模型。 首先比較不同到期期間下，不同模型評價誤差與價內程度的關係，發現不同到期期間買權在不同模型的評價誤差，於價外或價內時較低，但處於價平區間則出現較大的誤差，B-S模型傾向低估，而GEV模型比B-S模型相對來得準確多了；距到期日10、30天期的賣權亦有相同的結果，在價平區間B-S模型傾向低估，而GEV模型則傾向高估，但距到期日60、90天期的賣權則不論位於價內或價外，價平均產生較大的評估誤差。 本文檢視極端事件發生前後買權RND函數，由圖形的變化可以看出此價格的密度函數分配形狀比事件發生前更呈現負偏(左偏)。其中，形狀參數在極端事件發生前後皆由負值轉為正值，表示投資人認為市場有轉趨向下(downside)的情形。 最後，比較不同到期期間選擇權的隱含波動性與價內程度比是否具微笑波幅現象，發現買權随著到期日拉近，其微笑波幅愈明顯。 This article construct option pricing model based on Generalized Extreme Value distribution. Then, we use this model to discuss the skewness and excess kurtosis of returns in extreme event (i.e subsprime mortgage). In our empirical study, we used four different days to expiration’s Taiwan stock index optoin to evaluate the pricing peformances based on subsprime mortgage event. Empirical results reveal that GEV option pricing model is better than B-S option pricing model. We futrther compare the price bias of moneyness, it shows that the prices are lower in in-the-money and out of the money for both models. In addition, there is a larger bias when the options are at the money. The B-S model seems to overpriced and the GEV model is underpriced. The 10 and 30 days to expriation put options have also the same results. But 60 and 90 days to expriation put options have a large bias in in-the-money and out of the money. This article examines the shape of call option RND function on before and after some extreme events. The shape of distribution is more skewed negative which can be seen from the graph of the price density function. Among them, the shape parameters changes form positive to negative after the extreme events, indicating investors believe that the market has turned down (downside) of the case. In last, we compare the volatility smile effect of moneyness and find that call options are observious at nearing its expriation.
