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Application Of Mixed Fractional Brownian Motion In European Option Pricing

Posted on:2017-05-07Degree:MasterType:Thesis
Country:ChinaCandidate:T ZhangFull Text:PDF
GTID:2279330488487311Subject:Applied Mathematics
Abstract/Summary:PDF Full Text Request
Option, which also known as choice, is a derivative financial instrument. Option has started from the European and American market in the late eighteenth Century, but the development of options has been suppressed due to the incomplete system and some other factors. Until April 26th,1973, the Chicago Board Options Exchange (CBOE) opened for unified and standardized options contracts to obtain the considerable development of options trading.With the development of option trading, options are increasingly involved in various financial activities, the option pricing problems have been more and more concerned by scholars. The most famous European option pricing model was proposed by Fisher Black, Myron Scholes and Robert Merton (B-S model) in 1970s. The model on the market had made a series of assumptions, such as financial asset return rate obeys the lognormal distribution, the risk-free interest rate is constant, financial assets in the options within the validity period of no dividends and other income, the market has no friction, the options are European options.However, in the real financial market, some of these assumptions can’t accord with the reality. For example, the return on financial assets doesn’t obey the log normal distribution, but has the characteristics of "peak", "fat tail" and "self correlation". In this way, we can consider using fractal market to improve the B-S model, in order to get a European option pricing model which is much closer to the market.This paper has mainly talked about the pricing issue of the mixed fractional Brownian motion in European option. Through the introduction about the relevant preliminaries and the rigorous demonstration in detail, it has worked out the regular form of the option pricing formulas in the mixed fractional Brownian motion. It also has introduced the B-S model and the option pricing formulas of the fractional motion. With the empirical analysis in the ETF of SSE 50 data recently and verifying the results of three pricing formulas, the paper has proved that mixed fractional Brownian motion has a great effect on option pricing formulas in Chinese financial market.
Keywords/Search Tags:European Option Pricing, B-S model, fractional Brownian motion, Mixed fractional Brownian motion, Empirical Study
PDF Full Text Request
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