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Simulating geometric Brownian motion
created by:
Thijs van den Berg
(http://www.sitmo.com)
Simulating geometric Brownian motion. This equation is the exact solution of the geometrix brownian motion SDE.
List of symbols
Initial value at t=0 of geometric Brownian
Value of geometric Brownian motion at time t
Drift term
Volatility
Random sample from a normal (Gaussian) ditribution with mean 0 and standard deviation 1.
Related Equations
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Brownian Bridge »
Calibrating the Schwartz type 1 model »
Correlation between two points in time of geometric Brownian motion »
Expected value of a geometric Brownian motion raised to a power for S
Expected value of a geometric Brownian motion raised to a power for S>K »
Generating an Exponential distributed random number »
Generating Normal (Gaussian) distributed random numbers »
Generating Pareto distributed random number »
Geometric average in time, continously sampled »
Geometric average in time, discretely sampled »
Geometric Brownian motion SDE »
Joint high-low probability of geometric Brownian motion »
Probability density of geometric Brownian motion hitting a barrier for the first time at T »
Probability density of geometric Brownian motion at a fixed time »
Probability of the high of geometric Brownian motion »
Probability of the low of geometric Brownian motion »
Simulating an Ornstein-Uhlenbeck Process »
Simulating geometric Brownian motion with a cash dividend »
Simulating geometric Brownian motion with a stock dividend »
Simulating geometric Brownian motion with multiple cash dividends »
Simulating interest rates with the Vasicek model »
Simulating the Schwartz type 1 stochastic process »
Trinomial Tree, geometric Brownian motion »
Main Equations Index »
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