关于不确定汇率模型的亚式期权定价公式推导

doi:10.3969/j.issn.1000-1565.2019.05.002

河北大学学报(自然科学版) ›› 2019, Vol. 39 ›› Issue (5): 455-458.DOI: 10.3969/j.issn.1000-1565.2019.05.002

关于不确定汇率模型的亚式期权定价公式推导

高荣,王纯,张赞美

收稿日期:2019-04-25 出版日期:2019-09-25 发布日期:2019-09-25
作者简介:高荣(1992—),女,山东泰安人,河北工业大学讲师,博士,主要从事不确定微分方程和期权定价研究. E-mail:rgao@hebut.edu.cn
基金资助:
河北省社会科学基金资助项目(HB18GL036)

Establishments of Asian option pricing formulas for uncertain currency model

GAO Rong, WANG Chun, ZHANG Zanmei

School of Economics and Management, Hebei University of Technology, Tianjin 300401, China

Received:2019-04-25 Online:2019-09-25 Published:2019-09-25

摘要/Abstract

摘要： 亚式期权是一种重要的金融衍生工具,它是金融市场最受欢迎的路径依赖型期权之一,其收益取决于期权整个周期内标的资产的平均价值.由于风险的动态不确定性,因此假设外汇市场中的利率是一个不确定过程,其变化规律可由不确定微分方程来刻画.为了对冲外汇市场中的风险,银行拟定一个合同来赋予投资者以敲定价格购买外汇的权力,而拥有这项权利需要付出一定的代价.因此,本文以不确定外汇模型为基础研究了亚式期权问题,结合不确定理论和公平定价原则最终推导了几何平均亚式期权的定价公式.

关键词: 亚式期权, 不确定过程, 不确定微分方程

Abstract: Asian option is a significant financial derivative instrument, which is one of the most popular path-dependent options. Its income is decided by the average value of underly asset within the whole lifetime of the option. Influenced by the dynamic uncertainty of risk, the interest rate in foreign exchange market is assumed to be modeled by uncertain process and its law of change obeys an uncertain differential equation. In order to hedge against risks from the foreign exchange market, the bank provides a contract for investors to give them a kind of right instead of obligation to buy foreign exchange at a knock exchange rate. Naturally, for possessing such right, the investor needs to pay for the contract. Hence, based on the uncertain foreign exchange model, this paper studies the Asian option problem. Combining uncertainty theory and fair price principle, the pricing formulas of geometric average Asian option are deduced.

Key words: Asian option, uncertain process, uncertain differential equation

中图分类号:

高荣,王纯,张赞美. 关于不确定汇率模型的亚式期权定价公式推导[J]. 河北大学学报(自然科学版), 2019, 39(5): 455-458.

GAO Rong, WANG Chun, ZHANG Zanmei. Establishments of Asian option pricing formulas for uncertain currency model[J]. Journal of Hebei University (Natural Science Edition), 2019, 39(5): 455-458.

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关于不确定汇率模型的亚式期权定价公式推导

Establishments of Asian option pricing formulas for uncertain currency model

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