So, I have worked out getting the cumulative distribution of black scholes to
P(S<s)=N((ln(s/k)+(r+.5*sigma^2)t)/(sigma*t^.5)) since S follows GBM. Well What I am interested in finding the density function of S so I can find the second moment of S E(S^2) mannually by integrating xf(x)dx from 0 to infinity. I thought the density function would just be 1/(2Pi)^.5 e^-((ln(s/k)+(r+.5*sigma^2)t)/(sigma*t^.5))^2 /2 but from reading a few things online its not? And if what I read was wrong and I am right how the heck do you integrate something like this?
Thanks
P(S<s)=N((ln(s/k)+(r+.5*sigma^2)t)/(sigma*t^.5)) since S follows GBM. Well What I am interested in finding the density function of S so I can find the second moment of S E(S^2) mannually by integrating xf(x)dx from 0 to infinity. I thought the density function would just be 1/(2Pi)^.5 e^-((ln(s/k)+(r+.5*sigma^2)t)/(sigma*t^.5))^2 /2 but from reading a few things online its not? And if what I read was wrong and I am right how the heck do you integrate something like this?
Thanks
Deeper into Black Scholes than a black hole??
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