black scholes模型

分类号：索强：

编号：

理学硕｝：学何沦文

ＢＩａｃｋ—ＳｃｈｏＩｅｓ期权定价模型的修正

硕士研究生

指导教师Ｊ二扬郑晓阳教授

应用数学

孙广毅副教授学科、专业学位论文主审人

哈尔滨工程大学２００７年ｊ月

摘要

最近二十多年来．会融衍生证券在全球范围内获得迅猛发展，期权定价问题越柬越引起国内外数学家、金融学家的广泛重视。给期权合理的定价是期权交易的中心问题，因为交易主要是通过比较实际市场价格和期权真正价值进行的。在所有的衍生证券定价中，期权定价的研究最为广泛。期权定价问题是会融数学中的核心问题之一。１９７３年美国金融学家Ｂｌａｃｋ和Ｓｃｈｏｌｅｓ在有效市场和股票价格遵循几何Ｂｒｏｗｎ运动，且股票的预期收益率和波动率为常数的假设下，获得了著名的Ｂｌａｃｋ—Ｓｃｈｏｌｅｓ期权定价模型。Ｂ—Ｓ模型其实是一种理想的状态，在现实市场中，它的一些假设往往不满足。本文在Ｂ１ａｃｋ—Ｓｃｈｏｌｅｓ模型的基础上，通过改变Ｂ—Ｓ模型的基本假设，给出了几种基本的修ｎｉ模型及定价公式。改进后的模型使得股票价格行为更接近现实市场的运作规律，从而更有现实意义。

本文在这方面的主要工作有：

（１）首先在分析了期权定价理论的发展现状和前景以及相关理论的基础上，介绍Ｂｌａｃｋ—Ｓｃｈｏｌｅｓ期权定价

基于分数Black_Scholes模型的外汇期权定价及其评判检验

价格月刊

２００８２经济分析

６８

总第３６９期

基于分数Ｂｌａｃｋ－Ｓｃｈｏｌｅｓ模型的外汇期权定价及其评判检验

傅强王凯刘晓羽

【摘

要】笔者打破传统的有效市场假设，在假定外汇市场为分形市场的前提下，结合Ｂｅｎｄｅｒ和Ｅｌｌｉｏｔｔ等给出的欧

式未定权益的分数Ｂｌａｃｋ－Ｓｃｈｏｌｅｓ模型，建立了基于分数Ｂｌａｃｋ－Ｓｃｈｏｌｅｓ模型的欧式外汇定价公式。利用招商银行提供的外汇期权交易数据进行了实证检验，检验结果表明：基于分数Ｂｌａｃｋ－Ｓｃｈｏｌｅｓ模型的外汇期权定价公式的定价性能与定价精度都优于传统的外汇期权定价公式。【关键词】

外汇期权分形市场

分数布朗运动

定价偏差

【中图分类号】

Ｆ８３０．９【文献标识码】Ａ【文章编号】１００６－２０２５（２００８）０２－００６８－０３【作者简介】

傅强，重庆大学经济与工商管理学院教授，博士生导师，主要研究方向为金融数学和金融系统动力学；王凯，重庆大学数理学院硕士研究生，主要研究方向为金融数学与动力系统分析；刘晓羽，重庆大学数理学院硕士研究生，主要研究方向为金融数学与动力系统分析（重庆４０００４４）。

一、引言

业的一个重要任务。虽然我国各银行已开始推出个人外汇外

所属类别 所属内容 模型名称 模型描述

期权定价模型的检验 期权定价的基本原理 欧式看涨期权的 Black-Scholes 公式 标的资产价格遵循几何布朗运动的 Black-Scholes 原创设定已经成为 并将继续作为占支配地位的期权定价模型，所有其他模型都与它做比 较。对欧式看涨期权，Black-Scholes 公式可以写成本公式。BS

c模型公式

F ,T ; X , r , e

rT

ln F / X 1 2T 2 FN T

ln F / X 1 2T 2 XN T 式中 F 是标的资产的远期价格， T 是期权的到期时间， X 是执行价 格， r 是连续复利率， 是单位时间的瞬时条件方差，而 N2

变量说明

是

正态分布函数。

扩展方向

We discuss the evolution of black hole transients on the basis of a few systems that were intensively observed with the Rossi X-ray Timing Explorer. We focus on the global evolution and the observed state transitions. Rather than giving a numerical recipe

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aTheevolutionofblackholestatesJeroenHomanMITCenterforSpaceResearch70VassarStreet,Cambridge,MA02139,USAjeroen@space.mit.eduTomasoBelloniINAF/OsservatorioastronomicodiBreraViaE.Bianchi46,23807,Merate(LC),Italybelloni@merate.mi.astro.itAbstract.Wedi

This lecture reviews the black hole information paradox and briefly appraises some proposed resolutions in view of developments in string theory. It goes on to give an elementary introduction to the holographic principle.

BlackHolesandtheHolographicPrinciple

L´arusThorlacius

ScienceInstitute,Dunhaga3,107Reykjavik,Iceland

lth@hi.is

Abstract

arXiv:hep-th/0404098v1 14 Apr 2004Thislecturereviewstheblackholeinformationparadoxandbrie yappraisessomeproposedresolutionsinviewofdevelopmentsinstringtheory.Itgoesontogiveanelementaryint

We discuss the evolution of black hole transients on the basis of a few systems that were intensively observed with the Rossi X-ray Timing Explorer. We focus on the global evolution and the observed state transitions. Rather than giving a numerical recipe

5

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a

J

4

2

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95

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1

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/

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aTheevolutionofblackholestatesJeroenHomanMITCenterforSpaceResearch70VassarStreet,Cambridge,MA02139,USAjeroen@space.mit.eduTomasoBelloniINAF/OsservatorioastronomicodiBreraViaE.Bianchi46,23807,Merate(LC),Italybelloni@merate.mi.astro.itAbstract.Wedi

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Results of precise measurements of the periods of pulsars discovered in the central regions of globular clusters are shown to be approaching the capabilities of testing the existence of a central black hole. For example, in the case of M 15 the available d

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rtHubbleSpaceTelescope(HST)observationsofglobularclus-stersprovideauniquepossibilityofrevealingthenatureoftheira:centralregions.Doglobularclusterscontaincentralblackholesvorarewedealing

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Abstract:

In recent years, the endless stream of black life in the United States film and television has shown, Black English has also been widespread concern. This paper mainly expresses the sources of American Black English and complicated analyses the main features of Black English.

Key words:

Black English dialect features racialism

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EXPERIMENT 1 Black-Box Testing (1)

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The aims of this experiment included

? Be familiar with the common black-box test techniques

? To master the skills for designing the test cases by equivalence partitioning

method

? To master the skills for designing the test cases by boundary conditions

method

B. Experimental Contents

1. To test ADD (“+”) function of Windows Calculator in a personal computer.

（binary / decimal）

2. To test the registration function of Hotmail mailbox. 3. The requirements for t