# Simulating Asset Prices with a GARCH(1,1) Model

Simulating Asset Prices with a GARCH(1,1) Model

Independent, identically distributed, properly scaled Gaussian random numbers are the foundation upon which Brownian motion, geometric Brownian motion, and a wide variety of other diffusions are simulated. The GARCH model is different: the variance of today's return depends conditionally on (a) the variance of yesterday's return, and (b) the square of yesterday's return.