Study On The Pricing Of Look Back Options In Fractional Brownian Motion

Options are financial mathematics area of study of the most extensive one type of financial, while the option pricing is the core work.In order to meet the financial markets and the needs of different investors in the standard option contract based on the use of option theory and analysis methods, Look-back on options,which designed to create a path-dependent exotic options, it returns the due date dependent upon the options validity of the underlying asset price experiences the maximum or minimum value. Because of the strong path dependence, it makes the look-back option pricing is more complex than the standard option pricing.This article is a fractional Brownian motion to characterize the changes in stock prices, with Poisson jump process to characterize when there is big news when they arrive in greater volatility in the stock price. Main application of stochastic processes such as mathematical tools to discuss the fractional Brownian motion model and fractional- jump-diffusion model and the expected rate of return in the stock, volatility and risk-free interest rates are a function of time look-back on the context of option pricing problem the establishment of a look-back option pricing model,combined with Wick product theory is derived Looking back on option prices to meet the display expressions.