Option Pricing Models Driven By Sub-Fractional Brownian Motion And The Method Research

Option pricing is one of the important issues in financial mathematics.Since the classical pricing model Black-Scholes model was proposed,researchers usually use geometric or fractional Brownian motion to drive the underlying asset price,and some of the variables in the model are generally assumed to be constant,which makes the model ineffective in reflecting the complexities of real financial market conditions.For this reason,it is important to establish a reliable option pricing model,which makes the model to be more closely aligned with the characteristics of the actual financial markets,and the data to be more closely aligned with the option prices in the real financial markets.Based on the theories and methods of option pricing and sub-fractional Brownian motion,this dissertation studies three pricing models.Firstly,we establish a pricing model of Asian option with floating strike price driven by the sub-fractional Brownian motion.We obtain the sub-fractional partial differential equations for geometric Asian options by using delta-hedging method and It? formula.The pricing formula and call-put parity formula for geometric average Asian option with floating strike price are given by using Fourier transform method.Some numerical results are given to explore the relationship between different values of parameters on option prices.Secondly,we study the valuation of bid and ask prices for Asian options in the mixed sub-fractional Brownian motion regime.Within the framework of conical finance theory and distortion measure theory,we obtain the explicit formulas for the bid-ask prices of call and put Asian options by using Wang-transform and the permutation method.The numerical results show the impact of some parameters on bid-ask prices and bid-ask spread.Finally,we establish the compound option pricing model in the sub-fractional jump-diffusion model regime.By using Poisson jumps and cumulative probability distribution function theory,we obtain the expression of compound option price.We present numerical results under the influence of several parameters and compare the model with several commonly used option pricing models.