European Barrier Range Accrual Option Pricing Formula Deduction and the Corresponding American Range Option Numerical Value Simulation

European Range Accrual Option pricing and deviation Formula has been deduced through observing the foundational asset probabilistic distribution characteristics with help of Ito’s lemma, relaxing boundary assumption to infinity zero respectively, classical Black-Scholes option formula worked out. This paper subsequently articulates numerical value simulated computation algorithm using logic program language for corresponding demonstration. From a statistical point view, American range is not definitely more valuable than difference between their deviations significant.