Research On The Pricing Of Two Types Of Power Options Based On Fractional Brownian Motion In Fuzzy Environment

In this paper,based on the fractional Brownian motion in a fuzzy environment,two types of European call power options pricing problems with random strike prices are studied.Due to the obvious sharp peaks and thick tails and long-term correlation characteristics of asset returns,fractional Brownian motion can better describe changes in asset prices compared to standard Brownian motion.In addition,financial markets are characterized by volatility and insufficient information,and a random environment The parameters in the option pricing model such as risk-free interest rate and volatility cannot be an accurate data.The proposal of fuzzy theory has become one of the ways to solve this problem.It is against this background that this article takes into account the uncertainty At the same time,it includes both randomness and ambiguity.In a random environment,it also considers that the random execution price can reduce the risk to a certain extent.The pricing of two types of European power options is studied.The main content and conclusions include the following three aspects.The first aspect is the pricing of two types of European power options in random environments.Taking into account the "peak and thick tail" characteristics of financial asset returns,this paper uses fractional Brownian motion to describe the changing process of stock prices.At the same time,considering the random execution price,risk-neutral pricing is used to derive random execution under fractional Brownian motion.The corresponding analytical solutions are obtained for the pricing formulas of the two types of European call power options.The second aspect is the pricing problem of two types of European power options based on the random strike price of fractional Brownian motion in fuzzy environment.We consider that uncertainty includes not only randomness but also ambiguity.Therefore,we use the knowledge of fuzzy set theory to blur the risk-free interest rate,volatility and stock price,and obtain two types of European styles under two uncertain environments.The fuzzy price range of call power options is the end of this section.Considering that in order to facilitate investors'decision-making,this paper will also de-fuzzify the fuzzy price range obtained in this paper,and obtain the possibility of two types of European power options under uncertain environments.The third aspect is the use of Python for numerical simulation.Mainly studies the impact of two important parameters Hurst index H and confidence level ? on the prices of two types of European power options.At the same time,it also studies the stock price,execution price,risk-free interest rate and other parameters in the traditional Black-Schole model.The results of this article's pricing model are all in line with economic significance.In addition,in the last part of the numerical simulation,the model of this article is compared with the traditional model,which mainly includes the comparison of random and fixed execution prices,and asset prices in fuzzy environments.The model comparison of fractional Brownian motion and standard Brownian motion,and the comparison of the probability mean value in fuzzy environment and the traditional model option price in non-fuzzy environment.