European Option Pricing Based On The Stochastic Interest Rate Model

This thesis mainly discusses the problem of European option pricing based on thestochastic interest rate model, including the following aspects: stochastic analysis and optiontheory, the generation and background knowledge of Black-Scholes formula wherein theformula is satisfied by the price of any derivative security based on stock without dividend,the solution of Black-Scholes formula under the partial differential equation method and theequivalent martingale measure method, the discussion for European option pricing based onparticular stochastic interest rate model and the general stochastic interest rate model, as wellas in the more complex assumption, the derivation of European option pricing with thestochastic interest rate,paid dividend and jump-diffusion.The discussion of this thesis is based on the option pricing which takes stock asunderlying asset, and it focuses on the behavioral pattern of stocks. The Black-Scholesdifferential equation satisfying all derivative securities’ prices is deduced by forming asecurity group including a derivative security and a certain underlying stock meanwhileapplying the partial differential equation method and the equivalent martingale measuremethod and the relationship between the two method is given summarily. This thesis focuseson the improvement of inherent assumptions of the Black-Scholes model. It develops theoriginal option pricing formula based on the stochastic interest rate model whether the interestrate and stock is related or not. A closed form solution of European option pricing with thestochastic interest rate, paid dividend and jump-diffusion is given at the end of the thesis andit indeed expands the Black-Scholes model.