【作者】 成佩；

【导师】 严定琪；

【作者基本信息】 兰州大学 ， 应用数学， 2013， 硕士

【摘要】 浮动汇率制度的普遍执行,导致金融市场货币汇率风险日益暴露.作为重要避险工具的外汇期权地位更加突显.B-S公式很好地解决了期权的定价问题,但是它却依赖于标的资产服从正态分布.而分数布朗运动特有的长期性和自相似性与金融资产价格变化特性相吻合,使得用分数布朗运动来描述金融资产的价格变化更逼真.本文基于分数布朗运动建立了汇率满足的随机微分方程,利用分形积分理论,在风险中性定价原理下得到了新模型下的外汇期权定价公式.本文建立的新模型中假设本国和外国的无风险利率均是时间的函数,这使得新模型更贴近现实.另外本文还利用修正的R/S分析方法对我国外汇市场做了研究,结果表明我国外汇市场存在很明显的分形结构.这一结论为本文建立的模型提供了现实依据.最后本文通过实证对新模型和传统的外汇期权模型做了比较,表明分数布朗运动下的外汇期权定价更优越.更多还原

【Abstract】 Floating exchange rate system is generally carried out, which leads to exchange rate risk has become increasingly exposed in financial market. Foreign exchange option has become more prominent as a hedging tool.B-S formula solves the problem of option pricing well, but it depends on the underlying assets subject to the normal distribution. However, the fraction Brow-nian motion inosculates well with the change of financial assets price by its unique long-term and the like character, so it describes the change of financial assets price more realistic.This article established a stochastic differential equation of rate based on frac-tion Brownian motion, it used the theory of fractal integral and risk-neutral pricing to get a new model of foreign exchange rate option pricing. In the new model, we assume that the risk-free interest rate of domestic and foreign are functions of time, which makes the new model more close to reality. In addition, the modified R/S analysis is applied to study China’s foreign exchange market, the conclusion indi-cates that China’s foreign exchange market has a clear fractal structure. The result provides a realistic basis for the new model. At last, this article compares the new model and the traditional model by empirical analysis and gets that the new model is superior.更多还原