Research On Several Models Of Option Pricing In Sub-fractional Brownian Motion Regime

Option is an important part of the financial field.Risk is everywhere in investment transactions,and there are two choices to face risk: avoid it or take it.Option is a key tool for risk management and has the function of hedging and hedging risks.An option is an agreement by which the buyer acquires or sells quantitative underlying assets to the seller within a specified period of time and at a specified price.B-S model is the most widely used option pricing model.Its random driving source is Brownian motion,which cannot describe the characteristics of long-term correlation and self-similarity of stock price changes.Therefore,it is of great practical significance to find a new option pricing model to describe the trend of stock changes in real financial markets.According to the mathematical model and theoretical of option pricing,this paper constructs three pricing models.Firstly,the pricing model of European currency call options under the sub-fractional mechanism is founded.Using the Delta hedging method,we solve the definite solution of the foreign exchange option satisfaction under the model.Furthermore,the pricing formula of foreign exchange options and related numerical results are given.Numerical calculation shows that the option price under this model is lower than that under geometric Brownian motion under the same parameter values.In addition,the price of the European currency call option decreases as the strike price increases.Secondly,the pricing model of two-asset geometric Asian rainbow options in the sub-fractional Brownian motion regime is established.The pricing formula for two-asset geometric Asian rainbow options is derived by using partial differential equation method.Moreover,some numerical results are given.Numerical calculation shows that the price of the two-asset geometric Asian rainbow option decreases with the increase of the strike price.Finally,a time interval driven model driven by sub-fractional Brownian motion and Brownian motion is established.During the validity period of the contract,the random driving source is expanded from the traditional single source to two sources,which are driven by sub-fractional and Brownian motion respectively in different periods.Using the Mellin transform method,the pricing formula under this model is obtained and compared with classical B-S model and sub-fractional Brownian motion model.