The stochastic behavior of common stock variances Value, leverage and interest rate effects

Christie, Andrew A.

doi:10.1016/0304-405x(82)90018-6

Cited by 2,088 publications

(1,180 citation statements)

References 29 publications

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“…see Schwert (1989) and Figlewski and Wang (2000). Christie (1982) shows that by allowing the value of debt to change in the same direction as market capital, the leverage effect is weakened. Under risky debt, a negative market return leads to an increase in volatility, but the size of the impact declines as leverage grows.…”

Section: Time-varying Volatility Responsementioning

confidence: 99%

Estimating a Semiparametric Asymmetric Stochastic Volatility Model with a Dirichlet Process Mixture

Jensen

Maheu

2012

SSRN Journal

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In this paper, we extend the parametric, asymmetric, stochastic volatility model (ASV), where returns are correlated with volatility, by flexibly modeling the bivariate distribution of the return and volatility innovations nonparametrically. Its novelty is in modeling the joint, conditional, return-volatility distribution with an infinite mixture of bivariate Normal distributions with mean zero vectors, but having unknown mixture weights and covariance matrices. This semiparametric ASV model nests stochastic volatility models whose innovations are distributed as either Normal or Student-t distributions, plus the response in volatility to unexpected return shocks is more general than the fixed asymmetric response with the ASV model. The unknown mixture parameters are modeled with a Dirichlet process prior. This prior ensures a parsimonious, finite, posterior mixture that best represents the distribution of the innovations and a straightforward sampler of the conditional posteriors. We develop a Bayesian Markov chain Monte Carlo sampler to fully characterize the parametric and distributional uncertainty. Nested model comparisons and out-ofsample predictions with the cumulative marginal-likelihoods, and one-day-ahead, predictive logBayes factors between the semiparametric and parametric versions of the ASV model shows the semiparametric model projecting more accurate empirical market returns. A major reason is how volatility responds to an unexpected market movement. When the market is tranquil, expected volatility reacts to a negative (positive) price shock by rising (initially declining, but then rising when the positive shock is large). However, when the market is volatile, the degree of asymmetry and the size of the response in expected volatility is muted. In other words, when times are good, no news is good news, but when times are bad, neither good nor bad news matters with regards to volatility. JEL classification: C11, C14, C53, C58

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Section: Time-varying Volatility Responsementioning

confidence: 99%

Estimating a Semiparametric Asymmetric Stochastic Volatility Model with a Dirichlet Process Mixture

Jensen

Maheu

2012

SSRN Journal

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“…This can be explained by leverage and volatility feedback effects. Christie (1982) is one of the incipient researchers to explain the asymmetric behavior of the equity markets pertinent to leverage hypothesis, arguing that a price decrease in the stock would also decrease the market value of the firm, increasing its financial leverage and risk (volatility). Volatility feedback effects are best described by Campbell and Hentschel (1992) who vindicate that "news" escalate current volatility and surge future volatility as volatility dynamics exhibit persistency.…”

Section: Literature Reviewmentioning

confidence: 99%

Volatility Modeling and Forecasting of Istanbul Gold Exchange (IGE)

Gencer¹,

Musoglu²

2014

International Journal of Financial Research

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In this study, we model the volatility dynamics of Istanbul Gold Exchange with several GARCH models, which incorporate asymmetry and long-range dependence in the conditional volatility. We use daily spot prices of the gold exchange from January 4, 2006 to November 20, 2013. In addition, forecasting performances of the models are evaluated based on three commonly used measures. We examine the out-of-sample predictions for 1, 5 and 20-days ahead as the portfolio managers usually focus on longer horizons (20-days) as well as relatively short horizons (1 and 5-days ahead). The forecasting results point out the superior performance of EGARCH and CGARCH models. Hence our results provide useful information for investors and portfolio managers to consider asymmetric reactions to the news and long-range dependence property of the gold market in Turkey.

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“…It may be interesting to extend (1) to take into account some specific documented properties of the empirical returns, such at the "leverage effect" of a negative correlation between past returns and future volatility (Black, 1976;Christie, 1982;Figlewski and Wang, 2000;Bouchaud et al, 2001): E[r(t) 2 coming from the first term of r(t) multiplied by the cross-product of the two terms of r(t+1). This product of squares has a non-zero expectation with a sign controlled by that of c, which must thus be negative for the standard leverage effect to hold.…”

Section: Generalization To Other Bilinear and Trilinear Stochastic Momentioning

confidence: 99%

Properties of a simple bilinear stochastic model: Estimation and predictability

Sornette

Писаренко

2008

Physica D: Nonlinear Phenomena

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We analyze the properties of arguably the simplest bilinear stochastic multiplicative process, proposed as a model of financial returns and of other complex systems combining both nonlinearity and multiplicative noise. By construction, it has no linear predictability (zero two-point correlation) but a certain nonlinear predictability (non-zero three-point correlation). It can thus be considered as a paradigm for testing the existence of a possible nonlinear predictability in a given time series. We present a rather exhaustive study of the process, including its ability to produce fat-tailed distribution from Gaussian innovations, the unstable characteristics of the inversion of the key nonlinear parameters and of the two initial conditions necessary for the implementation of a prediction scheme and an analysis of the associated super-exponential sensitivity of the inversion of the innovations in the presence of a large impulse. Our study emphasizes the conditions under which a degree of predictability can be achieved and describe a number of different attempts, which overall illuminates the properties of the process. In conclusion, notwithstanding its remarkable simplicity, the bilinear stochastic process exhibits remarkably rich and complex behavior, which makes it a serious candidate for the modeling of financial time series among others. IntroductionDaily asset returns in liquid markets exhibit two key statistical properties: (i) price changes are not auto-correlated beyond a few minutes, but (ii) the absolute values of changes are autocorrelated over long time scales leading to long-term persistence of the volatility. Hsieh (1995) noted that nonlinear processes can generate this type of behavior while linear process cannot. Volatility clustering, also called ARCH effect (Engle, 1982) is a clear manifestation of the existence of non-linear dependences between returns observed at different lags. (FI)-GARCH (Baillie et al

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The stochastic behavior of common stock variances Value, leverage and interest rate effects

Cited by 2,088 publications

References 29 publications

Estimating a Semiparametric Asymmetric Stochastic Volatility Model with a Dirichlet Process Mixture

Estimating a Semiparametric Asymmetric Stochastic Volatility Model with a Dirichlet Process Mixture

Volatility Modeling and Forecasting of Istanbul Gold Exchange (IGE)

Properties of a simple bilinear stochastic model: Estimation and predictability

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