相依結構對多資產選擇權定價影響之實證分析

Abstract

本論文係探討相依結構對二元選擇權定價結果影響的實證分析。所謂二元選擇權，乃指兩個相異標的資產所衍生而得的奇異選擇權，其價格與兩個資產的價格變動及相依結構具有極大關聯。在此選取四組不同的金融指數作實證分析，其組成內容包含跨國家和跨資產，以期觀察在不同的相依結構下，對三種市場上較為廣泛交易的二元選擇權，其選擇權評價結果有何異同。論文中採用Copula-based GARCH模型作為定價方法，並利用適合度檢定選取出一最適相依結構，最後以蒙地卡羅模擬求得選擇權價格後，比較各相依結構下的選擇權評價差異。 研究結果發現，當標的資產相關程度愈強、選擇權到期日愈長、選擇權到期時的價格在價平附近與選擇權的報酬函數為二元彩虹選擇權時，在不同相依結構下的評價結果，其價格差異顯著性會愈高。故總結而言，相依結構的設定對二元選擇權的價格確實存在影響，在評價二元選擇權時是不可被忽略的一環。

Multivariate options have experienced significant development in the last decade, due to their excellent abilities for hedging the risk of multiple assets. The most important issue in the valuation of multivariate options is the dependence structure among these underlying assets. In this paper, we use copula-based GARCH model as pricing device to describe the dependence structures of underlying assets, rather than the traditional linear correlation and Gaussian assumptions to price multivariate claims. Particularly, the skewed-t GARCH model is applied to capture the marginal distributions of underlying financial assets. To compare the impact of difference dependence structures on option pricing, we perform Monte-Carlo simulation to simulate the bivariate option prices, and observe the error of option prices caused from different model dependence structures, time-to-maturities, strike prices and option payoff functions. We use goodness-of-fit tests to choose one dependence model that fit the empirical distributions best, and then the paired t-test is also implemented to determine whether the pricing errors are significant enough.