Modelling Short-Term Volatility with GARCH and HARCH Models

Normal mixture diffusion with uncertain volatility: Modelling short- and long-term smile effects

“…For liquid options, 3 The vast literature on estimating conditional densities of returns using models in the generalized autoregressive conditional heteroscedasticity (GARCH) family provides overwhelming evidence for nonconstant conditional volatility (Bollerslev, 1986(Bollerslev, , 1987Baillie and Bollerslev, 1989;Bollerslev et al, 1992Bollerslev et al, , 1994. Also, conditional heteroscedastic effects become more pronounced as the frequency of returns increases (Baillie and Bollerslev, 1990;Dacorogna et al, 1998). 4 These findings also concur with the central limit theorem: i.e.…”

Out of sample forecasts of quadratic variation

“…The model is inspired by the heterogeneity of agents operating in financial markets, and in particular to the different time horizons (such as daily or monthly) relevant for different investors (such as day traders or fund managers); see also Müller et al (1997) and Dacorogna et al (1998). Such heterogeneity could explain the strong positive correlation between volatility and market participation observed empirically.…”

Volatility dynamics and heterogeneous markets

“…As noted in the Introduction, several authors have suggested that volatility components may reflect the activities of heterogeneous traders, referred to as the 'heterogeneous markets hypothesis' (Guillaume et al, 1995;Dacorogna et al, 1998;Mu¨ller et al, 1997). That is, due to market participants possessing or facing different time horizons, such that 'short-term traders' evaluate the market at a higher frequency and have shorter memory than 'long-term traders'.…”

“…1 Guillaume et al (1995), Dacorogna et al (1998) and Mu¨ller et al (1997) adopt an alternative approach through the heterogeneous markets hypothesis, though antecedents of this approach can be found in the earlier observation that the presence of a unit root in conditional variance may imply the existence of a stochastic trend and a transitory component in returns volatility, as well as in the market microstructure literature dealing with different types of financial market trader.…”