選擇權訂價模型評估之損失函數探討

Abstract

本篇論文主要是在探討當我們在評比選擇權定價模型時，何種損失函數較為適當，損失函數的選擇是十分重要的，不同的損失函數隱含著不同的誤差結構，由於隨著不同的價內外程度與到期日，使得選擇權價格的可能範圍很大，造成以選擇權價格構成的傳統損失函數具有異質性的問題，而隱含波動度可能範圍穩定，由其所構成的損失函數不會有異質性的問題且較具有經濟意涵，因此較適合作為選擇權模型評比的準則，在本文中我們將以Black-Scholes模型與GARCH模型來驗證上述議題。

This thesis discusses the importance of the loss function when we evaluate the option pricing model. The choice of loss function is vital since it implicitly assumes a particular error structure. We discover that the use of the traditional loss functions imply a heteroskedastic error structure because of relatively wide range of option prices across moneyness and maturity. Unlike traditional loss function, implied volatility loss function does not have this problem and it have more economic meaning. We illustrate all these issues in an application of the ad hoc Black-Scholes model and the Heston-Nandi GARCH model to TAIEX options.