A Study Of Warrant Pricing Model Based On Fractal Theory

Now most of the researchers focus on the fractal B-S warrant pricing model to study the researches of warrant pricing models which based on fractal theory. As we all know, the reason that the hypothesis about the B-S warrant pricing model founded is that financial markets are normal. However, a large number of studies have the financial markets are fractal, but not normal, the fractal B-S warrant pricing model is presented in this case. Although it has a lot of the researches about fractal B-S warrant pricing model and it is fit for the fat tail characteristics of Chinese financial time series, with the August12,2011,’Changhong CWB1’ warrants stopped trading, marked the warrants which experienced a short period prosperity exit the stock market again. This shows the fractal B-S warrant pricing model in our country has not yet matured gradually improve, it has important theoretical and practical significance for researching the fractal B-S warrant pricing model.This article will be studied based on the multi-fractal theory of fractal BS warrants pricing model, and the fractal B-S warrant pricing model has been improved mainly from two aspects:First, improve the volatility of the fractal B-S warrant pricing model: Because a lot of researches show that Chinese stock market is a fractal market, the traditional methods of estimated volatility are no longer appropriate. In considering the financial time series with fat tail character-istics, biased, fundamental volatility clustering and leverage effect, the method associated with the multi-fractal will be applied fractal B-S warrant pricing model in this paper, using the built multifractal volatility (MFV) method to estimate the fractal B-S warrant pricing models volatility. Box-counting Method in multifractal analysis methods is used when building MFV models.Second, improve the Hurst exponent of the fractal B-S warrant pricing model:Today fractal B-S warrant pricing model are based on a single fractal to study the Hurst exponent and using a single fractal analysis method to estimate the Hurst exponent. However, various studies show that the price volatility of the stock market has multifractal characteristics. Therefore, this paper puts forward to study the generalized Hurst exponent based on multi-fractal instead of Hurst index based on a single fractal and use the improved multifractal detrended fluctuation analysis method (MF-DFA) in multi-fractal method to estimate the Hurst exponent.This paper takes Gezhou Dam warrants in China as an example, respectively for empirical based on the single fractal and the multiple fractal B-S warrant pricing models, and contrast the relative errors between the two. The empirical results show that the relative error of B-S warrant pricing model based on multi-fractal is smaller than the relative error of B-S warrant pricing model based on the single fractal and the stock price volatility of Chinese stock market is indeed significantly multiracial. Estimate the Hurst exponent based on the multi-fractal is more reasonable than based on the single fractal. And the use of MFV model volatility measure instead of constant volatility measure and generalized autoregressive conditional heteroskedasticity model volatility measure is effective. Finally, the research about the fractal B-S warrant pricing model is to study further and this paper studies the factors that influence the price of the warrants. What’s more, the paper analyzes the causes that the theoretical prices and the market prices of the warrants generated differences, then puts forward relevant policies recommendations and proposes a prospect about future research directions.