European option pricing under fuzzy environments
European option pricing under fuzzy environments
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DOI：
10.1002/int.20055
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发表时间：
2005-01
影响因子：
7
通讯作者：
Hsien-Chung Wu
中科院分区：
文献类型：
--
作者：
Hsien-Chung Wu
本文提出了模糊集理论在 Black-Scholes 公式中的应用。由于金融市场不时出现模糊波动，无风险利率、波动性和基础资产价格可能会出现不精确的情况。在这种情况下，自然要考虑模糊利率、模糊波动率、模糊股价。将引用模糊集理论中“分辨率恒等式”的形式来提出欧式期权的模糊价格。在这些假设下，t时刻的欧式期权价格将变成一个模糊数。这将允许金融分析师以他（她）可接受的信念程度选择欧洲价格。为了获得置信度，必须解决优化问题。 © 2005 Wiley periodicals, Inc. Int J Int Syst 20: 89–102, 2005。
The application of fuzzy sets theory to the Black–Scholes formula is proposed in this article. Owing to the vague fluctuation of financial markets from time to time, the risk‐free interest rate, volatility, and the price of underlying assets may occur imprecisely. In this case, it is natural to consider the fuzzy interest rate, fuzzy volatility, and fuzzy stock price. The form of “Resolution Identity” in fuzzy sets theory will be invoked to propose the fuzzy price of European options. Under these assumptions, the European option price at time t will turn into a fuzzy number. This will allow a financial analyst to choose the European price at his (her) acceptable degree of belief. To obtain the belief degree, the optimization problems have to be solved. © 2005 Wiley Periodicals, Inc. Int J Int Syst 20: 89–102, 2005.