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In fractional Brownian motion environment Martingale Option Pricing Analysis

Author: YuYanNa
Tutor: KongFanLiang
School: Harbin University of Science and Technology
Course: Applied Mathematics
Keywords: Fractional Brownian motion Equivalent martingale measure European Option Pricing
CLC: F830.9
Type: Master's thesis
Year: 2010
Downloads: 133
Quote: 0
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Abstract


In the financial statistics , Black-Scholes option pricing model to promote the general derivative securities contemporary financial statistics is an important issue . The martingale method in fractional Brownian motion environment for option pricing in mathematical finance research plays an important role. This article is for martingale method in fractional Brownian motion environment option pricing , do as follows: Firstly , with dividend payments for option pricing , the use of equivalent martingale measure theory in the equivalent martingale measure for the process under option ; By constructing suitable the approximation process , the fractional Brownian motion environment riskless asset ; European option using the terminal condition gives the fractional Brownian motion environment has a bonus payment option pricing formula. Secondly, in the actual financial markets , for investors to apply self- financing investment strategy, the existence of different borrowing rates . In fractional Brownian motion environment , derive the corresponding powers of different borrowing rates for European option pricing formula . Using the equivalent martingale measure theory to study the options formulas ; through fractional risk-neutral pricing formula construct appropriate BS model , gives a power with different borrowing rates for European option pricing formula . Moreover , taking into account the market price of the stock has long-range dependence and self-similarity , cyclical changes occur over time characteristics , built a fractional Brownian Motion Environment option pricing models. Martingale methods equivalent martingale measure theorem to obtain the equivalent martingale measure under the risk-free asset and risky assets satisfy equation ; utilization techniques integrating and expectations , as well as an appropriate model transformation, the fractional Brownian motion environment European power n -type option pricing formula. Martingale method for pricing options theory research that can better guide the tools people use mathematical theory , risk aversion in financial markets . This reduces investor risk in the investment , and financial markets stable and sustainable development has a wide range of theoretical and practical significance.

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