Home Services Equations Calculators LaTeX editor Forum Contact

Geometric Brownian motion SDE

Digg!
created by: Thijs van den Berg (http://www.sitmo.com)
Geometric Brownian motion SDE equation

The Geometric Brownian describes the most widely used model in finance. It is used to simulate the stochastic behaviour of stocks, currencies, futures. The value of this process is strick positive, St cannot get below zero.

List of symbols

Price process
Drift term
Volatility
W Wiener process (Brownian motion)

Related Equations
(r,s)-Fold Trimmed Mean Filters »  
Bayes's Rule »  
Binomial Tree, geometric Brownian motion: Cox, Ross, Rubinstein »  
Binomial Tree, geometric Brownian motion: Jarrow, Rudd »  
Binomial Tree, geometric Brownian motion: Tian »  
Binomial Tree, geometric Brownian motion: Trigeorgis »  
Black-Karasinski short term interest rate »  
Calibrating the Schwartz type 1 model »  
Chain rule for sequence of random variables »  
Characteristic function »  
Clewlow and Strickland jump-diffusion mean-reversion »  
Complex process »  
Conditional densities »  
Conditional distribution »  
Constant elasticity of volatility »  
Correlation between two points in time of geometric Brownian motion »  
Correlation coefficient »  
Cox-Ingersoll-Ross interest rate model »  
Expected value »  
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 »  
GARCH(1,1) stochastic volatility model »  
General stochastic differential equation »  
Geometric average in time, continously sampled »  
Geometric average in time, discretely sampled »  
Heston stochastic volatility model »  
Hull-White short term interest rate model »  
Independent random variables »  
Information content »  
Joint high-low probability of geometric Brownian motion »  
Jointly Normal Distribution density function »  
Laplace transform of pdf »  
Mean - Variance and r-moment about the mean »  
Merton jump-diffusion »  
Normal random variables »  
Ornstein-Uhlenbeck process »  
Orthogonal r.v.'s »  
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 »  
Random process X(t) and basis »  
Sample mean »  
Sample variance »  
Schwartz type 1 stochastic process »  
Schwartz type 2 stochastic process »  
Simulating geometric Brownian motion »  
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 the Schwartz type 1 stochastic process »  
Trinomial Tree, geometric Brownian motion »  
Vasicek stochastic process »  
Main Equations Index »
All text and equations on this page are freely available under the terms of the GNU Free Documentation License

Download

Word Pdf LaTeX

equation image:
.gif image