Warrants Pricing In A Mixed Fractional Brownian Motion Environment

Warrant is a special option, along with the introduction of stock index futures, options and other derivative products that will soon be launched, not even rule out re-issued warrants, so even now warrant has pulled out of the capital markets, warrants pricing study undoubtedly still have a strong practical significance.Since1973B-S option pricing formula appeared, it has become more and more widely in the Financial Field, it describes that the logarithm of the rate of return for financial assets subject to the standard normal and pricing of derivative products. However, in recent years a large number of empirical studies of financial markets show that financial asset is not fully in line with the characteristics of the geometric Brownian motion, its yield showed a peak fat-tailed distribution, and showing a long-term correlation between asset prices, this was in line with the characteristics of the fractional Brownian motion. Thus, we know that the fractional Brownian motion is more suitable for the description of the underlying asset price changes, so many scholars have proposed to replace the Brownian motion with fractional Brownian motion on the pricing of financial products. However, as long as it does not limit the investor’s investment strategy, fractional Brownian motion market will exist arbitrage opportunities. In order to eliminate arbitrage opportunities, Hu and Oksendal (2003) and Elliotts, Varderhoek (2003) extends the wick integral, and proves that fractional Brownian motion have no arbitrage under this integral, and gives Option Pricing in the fractional Brownian Motion Environment. But Bjork and Hult (2005) pointed out that Hu et al. Elliotte’s definition of self-financing and portfolio value does not have a reasonable economic explanation, so Cheridito (2001) applied the method of mixed fractional Brownian motion and proved mixed fractional Brownian motion is the no-arbitrage and consistent with the interpretation of economics. So this article studies warrants pricing in the mixed fractional Brownian motion environment.Due to the dilution effect,the pricing of warrants does not fully apply the option pricing formula, and many scholars have used the volatility of the stock instead of the volatility of the warrants, which have led to a reduction of the warrants pricing accuracy. In my article the pricing model taking into account the dilution effect of the warrants, draws on AndreyD.Ukhov (2004)studies of the equity value and volatility of the company’s two unobserved variables.Based on the contemplated conditional expectation and Fourier transform,this article solve warrants pricing in the mixed fractional Brownian motion environment, also extending to the underlying stock to pay the bonus case. Finally, through an empirical study of the warrants on the market, we know that the price of the mixed fractional Brownian motion model close to the market price,better than the traditional BS model.