The Roll (1977), Geske (1979) & Whaley (1981) option pricing model is defined as follows: 


C = call option value. S = spot price of the underlying asset. X = exercise price (strike). D = single discrete dividend. r = riskfree interest rate, expressed with continuous compounding. vol = volatility of the relative price change of the underlying asset. t = time to dividend payment measured in years (actual/365 basis). T = time to maturity measured in years (actual/365 basis). N(.) = cumulative normal distribution of (.). = cumulative bivariate normal distribution function with upper integral limits a and b, and correlation coefficient . I = critical exdividend stock price that equates the following: c(.) = value of European call with stock price I and time to maturity T.

Note that if or , it will not be optimal to exercise the option before maturity hence the price of the American call can be found by using the oBSdd( ) function. 
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