A new numerical method for pricing binary options in the CEV process

In order to study one of the valuation of the binary options in the constant elasticity of variance (CEV) process, by applying the Itô formula and no-arbitrage principle, derives the options pricing model and the differential equation of the options pricing model. Then, by means of semidiscretization for spatial variable, obtains the concrete semidiscretization numerical arithmetic scheme of the differential equation, conditional stability is proved, lastly numerical examples show that the algorithm is conditional stability and convergent.