The Journal of finance which a term(H'-(1+R)associated with a particular wr is raised is equal to the number of minus signs associated with the wr. Therefore if the valuation procedure is carried back to the present, the value of the option becomes (0)u(+R-H)-1+R 1…+(+R-H)H+-(1+R)+ u(1+R-H)}(H-(1+R) +(y/a(1+R-H)-(1+R)/[(H*-H1+R)y (A.5) Next, we must determine the value of the option at maturity. If the stock advances i times and declines(T-i)times, the price of the stock will be SoH*H on the expiration date. The option will be exercised if SoHH>X in which case, the maturity value of the option will be X Otherwise, the option will expire worthless Let the symbol a denote the minimum integer value of i in(A 6)for which the inequality is satisfied. This value is given by a=1+INt In(X/So)-TIn(H) In(H)-In(H where INT[ denotes the integer operator Thus, the maturity value of the option is given b ur=SH"H-""-Xii≥a T=0 if i< a (A8) By substituting(. 8)into(A. 5), one obtains a generalized option pricing equation (2)jsHr-x)(1+R-Hr-(1+R) T-1 (H*-H)(1+R) (A9) The Continuous Time model In the derivation of the continuous time model, we will determine the option rice when T+oo assuming that the mean and variance of logarithmic returns of the stock are held constant over the life of the option