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The Study of Option Pricing Model in Fractional Brownian Motion Environment

Author: HeChengJie
Tutor: DuXueZuo
School: Hefei University of Technology
Course: Applied Mathematics
Keywords: Fractional Brownian motion Gap Option Binary Options With Power Option Option Pricing
CLC: F830
Type: Master's thesis
Year: 2009
Downloads: 177
Quote: 0
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Abstract


Contingent claim pricing is one of the core issues of financial mathematics research , it relates to the modern finance , asset pricing theory , stochastic analysis and optimization of portfolio theory and modern mathematics theory and other disciplines . Effective risk management , it is necessary to correct the valuation of derivative securities , and how to determine the fair price of the derivative securities is that they exist reasonable and healthy development of the key . BS model of classical Brownian motion environment . However, empirical studies show that the stock price process has a long - term dependency and self - correlation , so in recent years , many scholars began to use the stock price process to meet both the nature of the fractional Brownian motion . Brownian motion is a special case of fractional Brownian motion . So, the option pricing study fractional Brownian motion environment more extensive and practicality . This thesis focuses on the study of finance in a number of the singular option pricing problem , establish the mathematical model of option pricing in a fractional Brownian motion environment , in this article the innovative work done : one derived fractional Brownian motion environment European Gap Option binary options pricing formula . The European Gap Option is a strange options, the yield to maturity is not comparing the execution price , but compared to another constant G ( gap) . Binary Options is a strange option where the payoff depends on the size of the maturity of the asset price and execution price . Second, we derive a power option pricing formula in the fractional Brownian motion environment . A power option is also a kind of exotic European options , Exponential European call option is due for payment function [h (S (T))? K] option , where h (x) = xα (α gt; 0, is a constant) . Thus , our promotional pricing of exotic options . .

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