The Dividend Asian Option Pricing In Fractional Brownian Motion

Option pricing theory is always one of the core research contents of finance. The traditional study of option pricing methods are based on the classical Black-Scholes options formula, and one of the assumptions of this formula is that stock price changes obey stochastic differential equation driven by standard Brownian motion.But in recent years,many scholars have found that the financial market bid asset prices have certain dependence or correlation in short-term or long-term, that is to say, previously hypothesis is too idealistic that the share prices obey standard Brownian motion conditions. The obtained results have very big deviation in actual financial activities. A more reasonable way is to use stochastic differential equation driven by fractional Brownian motion to describe the stock price, which is more actual in financial markets.Many scholars use fractional Brownian motion stochastic analysis theory studied option pricing. This paper using fractional Brownian motion new theory, discussed the Asian option pricing. Combining fitting - conditional expectation and fitting - martingale related theory, got geometry average Asian option pricing formula, generalized the option pricing model under the environment of fractional Brownian motion.Finally,considering the geometry average Asian option pricing formula is slightly complex,and arithmetic average Asian option can not get its analytical pricing formula since its contingent claimed characteristics rely on its rail, this word put forward a simple dividend Asian options pricing numerical simulation method under the environment of fractional Brownian motion.