# Project II - NUMERICAL AND SIMULATION TECHNIQUES IN FINANCE...

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NUMERICAL AND SIMULATION TECHNIQUES IN FINANCE PROJECT II Edward D. Weinberger, Ph.D., F.R.M Adjunct Assoc. Professor Dept. of Finance and Risk Engineering Code and debug a VBA function that computes the optimal parameters, α , β , and γ , for the GARCH(1, 1) model. This model results in bursts of volatility brought on by δ W t values of unusually large magnitude. This happens in the financial markets when important, unexpected events occur. The model is specified as follows, R t = σ t δ W t σ t 2 = α σ t -1 2 + β δ R t -1 2 + γ σ 0 2 where R t is the per-period return on some security over the period δ t , and δ W t is a normal random variable with zero mean and standard deviation δ t , independently chosen for each period. The fourth parameter, σ 0 , is the unconditional standard deviation of the returns, which can be estimated directly from the given data. Since α + β + γ = 1 is required for stability, therefore, only two parameters, say α and β , need to be estimated. As you will remember, these parameters can be found via the maximum likelihood

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Project II - NUMERICAL AND SIMULATION TECHNIQUES IN FINANCE...

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