Fractional Black-Scholes Option Pricing Model And Firm Value Assessment

In the context of the deepening maturity of China's capital market and the constantly open financial market,a large number of financial derivatives have emerged in recent decades.Financial derivatives are essentially financial contracts that regulate the rights and obligations of buyers and sellers,including but not limited to futures,forwards,swaps and options,and even two or more of the above four types of financial derivatives Mixed financial instruments.The emergence of financial derivatives undoubtedly enriched the capital market,increased market diversification and the ability to combat single risks,but triggered some new problems at the same time,the core of which was-the pricing of financial derivatives.Among all the financial derivatives,options are the most abundant and the widest range of applications.Therefore,a large number of economists have done a lot of research on the pricing of options for decades,and have made a series of fruitful achievements,of which the most Representative is the Black-Scholes option pricing model,which was born in 1973.This model constructs a portfolio using risky assets and riskless assets under the assumption that the underlying asset prices follow the geometric Brownian motion.In the rational person,Efficient Market Hypothesis,Ito Lemma,The risk-neutral pricing theory under the assumption of a series of assumptions,derived not out of the investor's subjective expectations of option pricing formula.Although Black-Scholes option pricing formula is a great landmark in the history of option pricing research,it is still not perfect.After decades of actual tests of capital market,many equity-like assets do not obey unbiased random walk,A large amount of financial practice proves that there is a phenomenon of "peak and fat tail" in the capital market.The underlying asset price has long-term dependence and self-similarity futures.That is to say,the capital market has the characteristics of fractal market.The partial fractional Brownian motion is more In line with the actual financial market fluctuations in stock prices.This paper will use the China Securities 100 Index 2007-2017 data for normality test,the actual data to prove that China's capital market has the characteristics of a fractal market,with the characteristics of long-term dependence and autocorrelation of the fractional Brown instead of the classic Black-Scholes model,we use the fractional Ito theorem to replace the original Ito lemma,and deduce the fractional Black-Scholes option pricing model in the fractional Brownian motion environment.Combining the traditional,This paper evaluates the enterprise value by fractional Black-Scholes option pricing model and compares the result with that under the classical Black-Scholes option pricing model,In order to consider the evaluation results under the new model.Finally,qualitative and quantitative sensitivity analysis of the various factors affecting the enterprise value under the option pricing model to examine the stability of the evaluation results.