I am trying to solve the Black Scholes SDE, but got really stuck. I have done most of the derivation but the integral seem intractable to me. The integrals look bit like the Normal Distributions PDF, but I am not sure how I am supposed to solve it. Could anyone help me with what method to use?
2026-03-29 10:55:35.1774781735
Black-Scholes SDE solution help
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You are almost there. Try doing a change of variables in the exponential part of the integral. Make it so that you get "$e^{-\frac{1}{2} x^2}$". Then you can relate this to the cdf of the normal distribution, ie $$ \Phi(z) = \int_{-\infty}^z \frac{1}{\sqrt{2\pi}} e^{-\frac{1}{2} y^2} dy. $$ Note also that, since the integrand is a pdf, $$ 1 - \Phi(z) = \int_z^\infty \frac{1}{\sqrt{2\pi}} e^{-\frac{1}{2} y^2} dy. $$