I'm doing a project about derivatives pricing before the Black-Scholes model was introduced. I have found a formula that had been used before the Black-Scholes model had been made. I'd like to compare the prices that the older equation gives for derivatives compared to the Black-Scholes model, but I can't solve the older equation. The equation is (1.1) in this link: http://www.ericbenhamou.net/documents/Encyclo/Pre Black-Scholes.pdf Specifically, I don't understand why there's a mean for N(x) or n(u) or how to find it. If someone could give some examples of how to solve the equation or how to solve it with excel, that would be great. Thanks.