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Autoregressive Heteroscedasticity Model and Its Variants 217 random draws from a standard normal distribution. Recall that a sta ...

218 The Basics of financial economeTrics moments exist and (2) they are constant and not time-dependent. That is, a covariance-s ...

Autoregressive Heteroscedasticity Model and Its Variants 219 predict the value of future variance of returns in function of past ...

220 The Basics of financial economeTrics If we require that c > 0 and that 0 < a 1 < 1, then the return process Rt is s ...

Autoregressive Heteroscedasticity Model and Its Variants 221 Figures 11.5 and 11.6 provide the plot of a simulated series of ret ...

222 The Basics of financial economeTrics 0 200 400 600 800 1,000 −5 −4 −3 −2 −1 0 1 2 3 4 5 Time Steps Returns FIGure 11.5 Simul ...

Autoregressive Heteroscedasticity Model and Its Variants 223 are predictable and we can determine explicit formulas to make pred ...

224 The Basics of financial economeTrics is noisy and unreliable. To avoid too many lags, Tim Bollerslev introduced a variant of ...

Autoregressive Heteroscedasticity Model and Its Variants 225 0 200 400 600 800 1,000 −3 −2.5 −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 Time ...

226 The Basics of financial economeTrics What Do ARCH/GARCH Models Represent? Thus far we have described ARCH and GARCH models a ...

Autoregressive Heteroscedasticity Model and Its Variants 227 similar models have been proposed. Table 11.1 lists some of the mos ...

228 The Basics of financial economeTrics volatility at time t is a weighted average of past squared volatilities and past square ...

Autoregressive Heteroscedasticity Model and Its Variants 229 Estimates of ARCH/GARCH Models ARCH/GARCH models can be estimated w ...

230 The Basics of financial economeTrics Application of GARCH Models to Option Pricing An option is a derivative instrument that ...

Autoregressive Heteroscedasticity Model and Its Variants 231 return distributions are known to be conditionally leptokurtotic, o ...

232 The Basics of financial economeTrics It is possible to define theoretically a multivariate ARCH/GARCH model called the VEC-G ...

Autoregressive Heteroscedasticity Model and Its Variants 233 The form of the process is similar to the univariate ARCH in equati ...

234 The Basics of financial economeTrics ■ (^) The simplest approach for measuring historical volatility involves cal- culating ...

235 Chapter 12 Factor Analysis and Principal Components Analysis a fter reading this chapter you will understand: ■ (^) What fac ...

236 The Basics of financial economeTrics Assumptions of Linear Regression First recall from Chapter 3 that all variables in a li ...