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Probability density of geometric Brownian motion at a fixed time

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created by: Thijs van den Berg (http://www.sitmo.com)
Probability density of geometric Brownian motion at a fixed time equation

This equation gives the probability density function of an underlying S at some future time t. The underlying behavior is geometric Brownian motion, has a present value S0, a yield (drift) of \mu, and volatility \sigma. The probability density function is has a lognormal distribution with mean \mu.

List of symbols

Probability of x
The value of the geometric Brownian motion process at time t
Volatility of the geometric Brownian motion
Drift of the geometric Brownian motion

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