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

state memory factor
variance memory factor
initial variance
random seed
view
volatility series
return series
asset price
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.
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