分形布朗运动下有交易成本的外汇期权定价

许莉莉1; 吴自力2

分形布朗运动下有交易成本的外汇期权定价

引用本文：许莉莉1，吴自力2.分形布朗运动下有交易成本的外汇期权定价[J].经济数学,2012,(3):64-69

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作者	单位
许莉莉1，吴自力2	（1.西安交通大学数学与统计学院，陕西西安 710049；2. 西交利物浦大学数学科学系，江苏苏州 215123）

中文摘要:研究了有交易成本的分形Black-Scholes外汇期权定价问题.基于汇率的分形布朗运动分布假设，运用分形布朗运动的性质和随机微积分方法，得到了欧式外汇期权价格所满足的偏微分方程.最后，建立离散时间条件下的非线性期权定价模型，并且通过解期权价格的偏微分方程给出了有交易成本的欧式外汇期权定价公式.

中文关键词:分形布朗运动外汇期权期权定价交易成本

Foreign Currency Option Pricing with Transaction Costs Driven by Fractional Brownian Motion

Abstract:We studied a fractional Black-Scholes formula for the option price of foreign currency with transaction costs. Based upon exchange rate’s fractional Brownian motion distribution, two partial differential equations of the European foreign currency option price were obtained by using the properties and stochastic calculus of fractional Brownian motion. In addition, by building nonlinear option pricing model on the condition of discrete trading times, we solved a partial differential equation of the European foreign currency options with transaction costs to get a relevant pricing formula.

keywords:fractional Brownian motion foreign currency options option pricing transaction costs

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