Rainbow Option Pricing-The Comparison of Fuzzy Theory and Traditional Stulz Model

碩士論文[[abstract]]本文自行挑選金融類、傳產類、電子類及混合類四種組合之二資產彩虹選擇權。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，並代入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，形成模糊化Stulz評價模型。績效結果顯示，模糊化Stulz模型評價結果較傳統Stulz模型穩定且有彈性。最後，求得各資產之Partial-Delta值，再根據Delta-Normal原則，計算每日避險損益，進一步提出每日損益之風險值。[[abstract]]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 is more stable. After calculating the Partial-Delta of each underlying asset and conduct the operation of hedging. In last, we can calculate the VaR via Delta-Normal principle