Asymmetry and Leverage in Conditional Volatility Models

Asymmetry and Leverage in Conditional Volatility Models

The three most popular univariate conditional volatility models are the generalized autoregressive conditional heteroskedasticity (GARCH) model of Engle (1982) and Bollerslev (1986), the GJR (or threshold GARCH) model of Glosten, Jagannathan and Runkle (1992), and the exponential GARCH (or EGARCH) model of Nelson (1990, 1991). The underlying stochastic specification to obtain GARCH was demonstr...

Asymmetry and Leverage in Stochastic Volatility Models: An Exposition

The accurate specification and modelling of risk are integral to optimal portfolio and risk management. In this context, a wide variety of conditional and stochastic volatility models has been used to estimate latent volatility (or risk). In both the conditional and stochastic volatility literature, there has been some confusion between the definitions of asymmetry and leverage. This paper exam...

Asymmetry and Leverage in Realized Volatility

Exponential Conditional Volatility Models

The asymptotic distribution of maximum likelihood estimators is derived for a class of exponential generalized autoregressive conditional heteroskedasticity (EGARCH) models. The result carries over to models for duration and realised volatility that use an exponential link function. A key feature of the model formulation is that the dynamics are driven by the score. Keywords: Duration models; g...

Arch Models and Conditional Volatility

w t here {e } is independent white noise. The width of the forecast interval is proportional to the square r root of the one-step forecast error variance, var [x − f ] = var [e ] =σ , a constant. On the othe n +1 n , 1 n +1 e t i hand, actual financial time series often show sudden bursts of high volatility. For example, if a recen nnovation was strongly negative (indicating a crash, etc.), a p...