Option Pricing Of A Jump-Diffusion Model With Multiple Sources Jumps

In modern finance,the option pricing theory is one of core problem and an importantpart in finance. In1973, Black and Scholes obtained the famous Black-Scholes optionpricing formula by partial differential equation theory, which made breakthroughcontribution for the research of the option pricing theory. For traditional Black-Scholesformula, many scholars also gave a lot of amendment and abundance. One of them is theoption pricing of jump-diffusion model.In this paper, it was assumed that stock price subject to the jump-diffusion processinfluenced by multiple source of jumps. New jump-diffusion model was established byrenewal process whose renewal spacing subjected toΓ (α,λ)distribution, derived optionpricing formulas.Main content is following:Firstly,it was assumed that stock price was subject to the jump-diffusion processinfluenced by multiple sources of jumps under stochastic interest rate. New jump-diffusionmodel was established by innovation process. By martingale measure transformation andIto formula,European option pricing formula of jump-diffuse model with stochasticinterest rate was derived,the parity relation between call option and put optionwasobtained. The results also were expand to the case of stock paided continuous dividend.Secendly, introducing Vasicek interest rate model into the jump-diffusion model,establishing new jump-diffusion model. By martingale measure transformation and Itoformula,European option pricing formula of jump-diffuse model with stochastic interestrate was derived, the parity relation between call option and put optionwas obtained. Theresults also were expand to the case of stock paided continuous dividend.Finally, it was assumed that stock price was subject to the iump-diffusion processinfluenced by multiple sources of jumps under stochastic interest rate. By martingalemeasure transformation and Ito formula, obtained four kinds of compound options andreset option.