Geometric Average Asian Options Pricing Model Based On Fraction Brownian Motion And Its Empirical Study

Along with the improvement of demand on the complexity in money market, it is difficult to satisfy the special needs of customers by only using the standard option. In order to satisfying the demand of markets and customers, many financial companies not only designed European options and American options but also devised a great deal of new breeds which derive from standard options. We call it exotic options. Asian option is the typical kind.How to use reasonable mathematical model to price Asian option comes important problem to investor using option to hedge risk of exchange rate. So, in financial field, the pricing problem of option becomes one of important fields of theory and practice research. This paper assumes that the stock return don't obey standards Brownian Motion, but general fractional Brownian Motion, and on this basis, gets the pricing model of geometric average Asian option.To modify the actuarial formula put forward by Bladt and Rydberg,an actuarial approach is proposed in view of evaluating actual losses and corresponding probability distribution to quantitatively cheek the price composition of geometric average Asian option,thus developing an option pricing model to deduce further the formula under the hypothesis of underlying asset price driven by fractional Brownian Motion when the asset has not dividend-paying or has dividend-paying.This paper also takes the Wuhan steel Warrant JTP1and the Bashan steel Warrant JTB1 as an example, calculates two kinds of warrant theory pricing using Fractional Geometric Average Asian option price model, and compared with the actual market price, obtained two kinds of warrant price deviation. Through carries on the static statistics and the dynamic analysis to the price deviation, discovered that the price deviation of the Bashan steel warrant is unstable, stochastic, using the theory price forecast that the market price is meaningless, the market plunge factor is the primary cause to create this result. The price deviation of the Wuhan steel warrant is stable; the theory price can be used to forecast the market price.