On Leverage in a Stochastic Volatility Model

By Jun Yu. 2005

451 citations recorded by the source corpus.

This paper is concerned with specification for modelling financial leverage effect in the context of stochastic volatility (SV) models. Two alternative specifications co-exist in the literature. One is the Euler approximation to the well known continuous time SV model with leverage effect and the other is the discrete time SV model of Jacquier, Polson and Rossi (2004, Journal of Econometrics, forthcoming). Using a Gaussian nonlinear state space form with uncorrelated measurement and transition errors, I show that it is easy to interpret the leverage effect in the conventional model whereas it is not clear how to obtain the leverage effect in the model of Jacquier et al. Empirical comparisons of these two models via Bayesian Markov chain Monte Carlo (MCMC) methods reveal that the specification of Jacquier et al is inferior. Simulation experiments are conducted to study the sampling properties of the Bayes MCMC for the conventional model

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/8af68cc4c3171e59e1f7f153f5b329e983b5438e

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Citations in the corpus

Multivariate Stochastic Volatility Models: Bayesian Estimation and Model Comparison (2006, methodology): “…MCMC software called BUGS (Bayesian analysis using Gibbs sampler) developed by Spiegelhalter et al. (1996).1 Since then, BUGS has been employed to estimate univariate SV models in a number of studies (for example, Berg et al., 2004; Lancaster, 2004; Meyer et al., 2003; Selçuk, 2004; Yu, 2005).”
Bayesian semiparametric stochastic volatility modeling (2010, background): “(2), ht ⊥ yt assumes away any leverage effects (see Jacquier et al., 2004; Yu, 2005; Omori et al., 2007).”
The Leverage Effect Puzzle: Disentangling Sources of Bias at High Frequency (2011, unknown): “Various discrete-time models with a leverage effect have been estimated by Yu (2005).”
Monte Carlo methods for estimating, smoothing, and filtering one- and two-factor stochastic volatility models (2006, background): “On the other hand, Yu (2004) finds in favor of the Euler-scheme timing (using S&P 500 index data from 1980–87 and a Bayesian estimator), so this result may not be robust.”
EGARCH, GJR-GARCH, TGARCH, AVGARCH, NGARCH, IGARCH and APARCH Models for Pathogens at Marine Recreational Sites (2013, background): “Jun Yu [9] and Siourounis [10] also preferred the non-normal distribution.”
A Semiparametric Stochastic Volatility Model (2012, unknown): “Our model extends the specification studied in Harvey and Shephard (1996), Yu (2005) and Omori et al. (2007).”
Multivariate stochastic volatility (2009, methodology): “Finally, Asai and McAleer (2004a) proposed a more general model which nests both the model of Yu (2004b) and the AL model as special cases.”
Stochastic Volatility of Volatility and Variance Risk Premia (2013, unknown): “…correlation between asset returns and volatility has been found in many empirical studies, see e.g. Black (1976), Christie (1982) and Nelson (1991) among others and,more recently, by Harvey & Shephard (1996), Bouchaud et al. (2001), Tauchen (2004, 2005), Yu (2005) and Bollerslev et al. (2006).”
An Analytical Formula for VIX Futures and its Applications (2012, methodology): “pdf Meyer & Yu (2000) illustrated the BUGS implementation for a stochastic volatility model using a time series of daily Pound/Dollar exchange rates.”
The Analysis of Stochastic Volatility in the Presence of Daily Realised Measures (2011, background): “Although this correlation may be present in some empirical settings due to leverage effects at higher frequencies, Yu (2005) argues that the specification of a negative dependence between ηt and εt+1 brings important theoretical drawbacks to the SV model.”
Inference for Lévy‐Driven Stochastic Volatility Models via Adaptive Sequential Monte Carlo (2011, methodology): “Another key component of the SVVG model is the modelling of leverage (see Griffin & Steel, 2006 and Yu, 2005, for recent discussions in a Bayesian modelling context).”
Hedging emerging market stock prices with oil, gold, VIX, and bonds: A comparison between DCC, ADCC and GO-GARCH ☆ (2015, unknown): “effect, although the effect is generally asymmetric (Yu 2005).”
Multivariate Stochastic Volatility: A Review (2006, background): “However, the argument of Yu (2005) regarding the leverage effect also applies to the model in (9).”
Nonparametric Estimation of the Leverage Effect: A Trade-Off Between Robustness and Efficiency (2017, unknown): “…their estimation involves either the Markov chain Monte Carlo algorithm or particle filters, see, for example, Jacquier, Polson, and Rossi (2004), Yu (2005), Pitt, Malik, and Doucet (2014), and Eraker (2004), or moment- or likelihood-based approaches, see, for example, Harvey and Shephard…”