應用模糊化Stulz模型於彩虹選擇權之評價

Pricing Rainbow Options Based on the Fuzzy Pattern of Stulz Formula

李沃牆(Wo-Chiang Lee) ； 黃淑菁(Shu-Ching Huang)

《真理財經學報》 13期 (2005/12) Pp. 23-42

https://doi.org/10.29963/TOJEB.200512.0002

摘要

本文挑選金融類、傳產類、電子類及混合類等四種組合來設計兩資產彩虹選擇權。根據過去學者研究之結果，以準蒙地卡羅法（Sobol低差異序列）模擬標的資產價格，再以MGARCH模型估計波動率，又採用移動相關係數，代入Stulz評價模型，如此便可得到彩虹選擇權的理論價格。接著，藉由模糊化標的資產價格、波動率、相關係數以及距到期期間，創新建立模糊化Stulz評價模型。並檢定出該模型與傳統Stulz模型之評價結果有顯著差異，表示模糊化Stulz評價模型可用於彩虹選擇權之評價。

關鍵字

彩虹選擇權 ； 準蒙地卡羅法 ； Sobol低差異序列 ； MGARCH ； 模糊理論

並列摘要

In this article, we design four kinds of two-asset rainbow option, namely finance, conventional industries, electronic, mixed finance with electronic rainbow option respectively. In our empirical study, we use Quasi Monte Carlo Method for the simulation of underlying asset price. Additionally, we utilize MGARCH model for estimating volatility and put the moving correlation coefficient into pricing model. Then, we may obtain rainbow option's theory price. Furthermore, we consider the fuzzy stock price, fuzzy volatility, fuzzy correlation coefficient and fuzzy maturity as input variables. Then, the fuzzy pattern of Stulz formula is proposed in this paper Empirical result shows that the Fuzzy-Stulz Model can be applied in rainbow option pricing.

並列關鍵字

Rainbow Option ； Quasi-Monte Carlo Method ； MGARCH ； Fuzzy Theory.

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