應用合適的損失函數於選擇權模型評價:避險績效

Abstract

在這篇論文裡，我們研究在評比選擇權訂價模型時，不同損失函數的適用性。我們的分析顯示用一個合理的評價標準去衡量不同模型間相對優點是相當重要的，基於避險者的角度，我們建議使用避險誤差作為損失函數來評定樣本外的績效。以台指選擇權為資料，用Black-Scholes模型描述三種不同形式的誤差並和CEV模型做比較，實證結果發現不適當的評比標準反而會使較好的模型被拒絕，因此選擇一個恰當的損失函數是必需的。

In this thesis, we investigate the adequacy of different loss functions when evaluating option pricing models. Our analysis shows that it is important to have a reasonable yardstick to assess the relative merits of competing models. Based on the viewpoint of a hedger, we recommend the hedging error to be the loss function in judging out-of-sample performance. We illustrate the effect on the three types of error in an application of the Black-Scholes model to TAIEX index options and compare with the constant elasticity of variance model. Our empirical results show that a better model may be rejected when using an inappropriate criterion. Thus, it is vital to choose a relevant loss function.