應用自組織映射神經網路於歐式選擇權定價模型之研究-以台灣指數選擇權為例

Abstract

著名的Black-Scholes 選擇權定價模型為目前業界與學界最常使用的選擇權定價模型，但是B-S模型中假設變異數為固定值且標的物資產報酬之變動服從對數常態分配，並不符合現實市場上的實際情況，使得其理論價格有所偏差。雖然後續模型的出現幾乎都是修正B-S模型的假設而生，但就目前看來，仍無一較適用的修正模型能夠完整改善B-S模型中不合理的假設。

近年來在人工智慧上的研究發現，自組織映射神經網路能將高維度資料間之複雜非線性關係轉換成低維幾何關係，並具有鄰近區域之拓樸結構，提供視覺化功能輔助決策者決策的特性，使其在獲取資料特徵值與內部結構上表現相當優異，相當適合做為金融環境資料分析之用。過去國內外的研究中對於使用自組織映射神經網路於選擇權定價模式修正方面較少著墨，故本研究嘗試使用標的物資產價格的歷史實際報酬率機率分配，提出以自組織映射神經網路為基礎的選擇權定價模式，修正B-S模式中視波動性為固定常數及股價服從隨機行為之不合理假設。

最後，本研究以台灣指數選擇權作為實驗對象進行實證分析，亦證明了本方法學所計算出的選擇權實驗價格比B-S理論價格要來的更合理，更值得作為投資人交易選擇權的參考價。

The Famous Black-Scholes option pricing model (B-S model) is the most popular option pricing model until now. However, the assumptions, don’t approach the real market in B-S model, lead to inaccurate price. Although follow-up researches had focused on modifying those assumptions, inaccuracy still exists.

Recent studies had introduced that AI, has significant efficiency in dealing with complex problems, have been used to solve financial issues. This study proposed a innovative pricing model that applying Self-Organizing Map (SOM) and considering the real payoff distribution of the underlying asset. The Model modifies unreasonable assumptions which asset volatility is constant and asset price follows stochastic process in B-S Model.

This study uses TAIEX Option as research target. Empirical analysis demonstrates that the price calculated by this model is more accurate than B-S model.