Abstract
Abstract Using the stochastic differential equation driven by the composite Poisson process of mixed fractional Brownian motion, the price model of a mixed jump-diffusion fractional Brownian motion environment is established. Under the condition of Merton’s assumption, the Cauchy initial value problem of stochastic differential equations is iterated. The method is estimated, and the Merton formula of the European put option under the mixed jump-diffusion model is obtained, and the call-back option and the bearish option pricing formula of the mixed jump-diffusion fractional Brownian motion European floating strike price are given.
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