| The pricing of financial derivatives is the core problem in modern financial field.Option pricing is the basis and core content of the pricing of financial derivatives.Volatility is one of the most important factors in option pricing.Applying volatility model to option pricing can improve the accuracy of option pricing.The research shows that the single-factor volatility model is still too limited to describe the term structure of volatility and the “volatility smile” time variation.Therefore,the multi-factor volatility model is of great significance in the study of option pricing.This paper studies option pricing based on stochastic differential equations,stochastic volatility and uncertainty theory.Firstly,we study the pricing of American put options when the underlying asset price process satisfies the multi-factor Heston stochastic volatility model.By using the basic theory of stochastic differential equation,the existence and uniqueness of the solution of the model are proved,and the American put option pricing can be obtained by using LSM algorithm.Combined with the multi-factor Heston stochastic volatility model,the influence of maturity time and strike price on the option price is studied,and the rationality and effectiveness of the model in American put option pricing are proved.Secondly,under the condition that the underlying asset price process satisfies the multi-factor uncertain volatility model,the pricing problem of European call and put options is studied.For the uncertainty of the model,using the basic theoretical knowledge of uncertain differential equation,according to the European call and put option pricing formula under the model,combined with the multi-factor uncertain volatility model,this paper studies the impact of the strike price and the underlying asset price on the option price,and proves the rationality and effectiveness of the model in European option pricing.It points out a new direction for the research of option pricing. |
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