What is GEOMETRIC BROWNIAN MOTION?

A lognormal, continuoustime STOCHASTIC PROCESS where the movement of a variable, such as a financial ASSET price, is random in continuous time; the instantaneous return (defined as the change in the price of the variable divided by the price of the variable) has a constant MEAN and VARIANCE. Certain DERIVATIVE pricing methodologies are based on the Geometric Brownian motion process.

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