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