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Pricing Barrier Options in a Fractional Brownian Motion Envrionment

Author: HuoHaiFeng
Tutor: DengGuoHe
School: Guangxi Normal University
Course: Probability Theory and Mathematical Statistics
Keywords: Fractional Brownian motion European , American barrier options PDE Quadratic approximation method Difference method
CLC: F830.9
Type: Master's thesis
Year: 2009
Downloads: 41
Quote: 1
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Abstract

Global financial markets in recent years has been the rapid development of the financial market transactions and transaction prices more flexible singular option (Exotic Options, also known as path-dependent options or non-standard option), such as: barrier options, Asian options and lookback options, and financial institutions are continuing to launch new combination of financial derivative products to the pricing of these products has been one of the hot topics of research in the field of financial mathematics, modern financial theory is applied to the actual one of the core academic values ??and social and economic significance is very obvious and we know, the reality of financial markets, effective market model has important implications for the decision-making of investors, financial risk management and hedge because of the classic Black -Scholes model deficiencies in the description of the market system variable, many to promote classical model of the market model is widely used, such as fractional Brownian motion model, Levy processes, stochastic volatility model and a large number of empirical studies have shown that the fractional Brownian motion characterize model of market price behavior model than the standard Brownian motion, Levy processes more in line with the a realistic price movement characteristics. thus it became one of the focus of current research model, but not many option pricing research in this area, which is due to scores times the theory of stochastic analysis of Brownian motion is still in the development stage. barrier options (Barrier Options) is one of the most active trading in the financial derivatives market today exotic options, cheaper than mass-option price, the risk is small, so the barrier options increasingly favored by investors. barrier option is a path-related options, it's final income depends on the path of the underlying asset price changes and options contracts to take effect when the underlying asset prices hit obstacles provisions or failure, so barrier options have a rich structure of income if the underlying asset price touches obstacles provisions and options contracts in force, known as the knock-barrier options (Knock-in-Options) knockin barrier options can be divided into four: rise knockin The bullish (Up-and-in Call Options), rose knockin bearish (Up-and-in Put Options), (Down-and-in Call Options) decreased knockin bullish, dropped knockin bearish (Down-and-in Put Options). underlying asset prices touched prescribed obstacles, options contracts invalid options (Knock-out-Options) called Knock knock out barrier options can be divided into four categories: rising knockout bullish (Up-and -outCall Options), rising knockout bearish (Up-and-out Put Options), dropped knockout bullish (Down-and-out CallOptions) decreased knocked bearish (Down-and-Out Put Options) This article assumes that the underlying stock price meet the fractional Brownian motion to discuss the European, American barrier options pricing, including major work: The first chapter introduces prior knowledge and Fractional Brownian motion under the meaning of the Option Pricing on the European, American barrier options pricing study of the status quo at home and abroad, topics basis and structure of the paper. discuss fractional Black-scholes European barrier option pricing model can not give fractional Brownian motion, maximum and minimum values ??of the probability distribution, this paper The European decline knock bullish barrier options pricing partial differential equations deduced display solutions, and thus given the option of remaining seven European barriers to pricing display solution, and bullish - bearish parity, these results fully covered when Hurst parameter H = 21:00, the corresponding results of the classic Black-Scholes model. Finally, numerical calculation and risk analysis. third chapter of fractional Black-scholes model American barrier options pricing, the first classic Black-Scholes model of American style options quadratic approximation method is extended to the case of fractional Black-scholes model, and further use of the quadratic approximation method to study the American Barrier Option Pricing, American barrier options prices approximate the optimal solution, as well as options exercise boundary satisfy the equation. Finally, using numerical analysis the impact of the the H parameters on the option price and the optimal exercise boundary, and application of the the display difference method test approximate solution of the accuracy of the results. fourth chapter summarizes the main work and to be further research.

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