The Stochastic Volatility Option Pricing Model With Mixed Fractional Brownian Motion

In recent years,the design,pricing and application of financial derivatives are the emerging financial industry projects.Option pricing is an important position in various researches of financial derivatives and has constituted the core content of financial mathematics.Two models are proposed in this paper.The MFAVS model uses the advantages of hybrid fractional Brownian motions and embeds the real-time rolling volatility,which can more accurately describe the fluctuations in the financial market and is more in line with the actual situation.Another FBMLHW model combines fractional Brownian motion with stochastic volatility and derives the pricing formula suitable for multi-dimensional asset options.The article clearly illustrates the relevance of the two models and their practical application background.Volatility is one of the important factors that affect the pricing of options.The article uses the GARCH and SV models to simulate the volatility,and combines the real-time rolling ideas to establish a one-dimensional option pricing model-MFASV.Specific examples are given to verify the MFASV model.The effectiveness of the method,using the data calculated by the model and the market truth,is compared by the loss function of the mean squared error,Obviously know that the real-time rolling volatility estimate is much better than the fixed-constant volatility.Finally,the effectiveness of the MFASV model is deduced.