Download 1. “Dissecting the Market Pricing of Return Volatility." Torben

1. “Dissecting the Market Pricing of Return Volatility."
Torben ANDERSEN (Kellogg Management School, Northwestern University, Chicago, USA) and Oleg
Bondarenko (University of Illinois at Chicago, USA).
Abstract:
In recent years, markets for direct trading of realized return volatility have emerged. A critical
theoretical backdrop for these developments is the model-free implied volatility which can be computed
from the full cross-section of options written on the underlying asset price. This notion underlies the VIX
index released by the Chicago Board of Option Exchange which prices the S&P500 equity return variation
over the coming month under the pricing (or Q) measure. We can also approximate the realized return
variation and its future expected value under the actual (or P) measure via high-frequency data
(Andersen, Bollerslev, Diebold and Labys (2003)). Hence, market premiums for variance risk, given by
the difference of realized variation under Q and P, may be obtained. The corridor variance splits the
expected return variation over the month into the expected return variation over specific price ranges
for the underlying asset. Carr and Madan (1998) introduce this concept and show it may be priced
similarly to the regular variance swap contract. We note that a similar decomposition of actual realized
return variation can be obtained from high-frequency data on the underlying asset. Thus, one may
investigate where the risk premium resides within the risk neutral density. We focus on the market price
of variance risk on the downside versus upside, i.e., the difference between the (expected) return
variance under the Q and P measures for periods when the index price is below versus above the
starting price of the month. This as a quantitative measure, backed by formal theory, of the timevarying market risk premium manifest in the smirk or skew of Black-Scholes implied volatilities for
equity indices. The findings are striking. The actual realized return volatility experienced during “up
states” and “down states” relative to the monthly opening index equity price is similar while, for the
corresponding quantities under the Q measure, the expected down state volatility exceeds that of the up
state by a factor of two-to-one. Moreover, a long position in the down variance swap contract has
negative returns on the order of 45% per month while the up variance swap returns are near zero.
2. “Expected Stock Returns and Variance Risk Premia”
Tim BOLLERSLEV (Duke University, USA) and Hao Zhou (Federal Reserve Board, Wahington DC, USA)
Abstract:
We find that the difference between implied and realized variation, or the variance risk premium, is able
to explain more than fifteen percent of the ex-post time series variation in quarterly excess returns on
the market portfolio over the 1990 to 2005 sample period, with high (low) premia predicting high (low)
future returns. The magnitude of the return predictability of the variance risk premium easily dominates
that afforded by standard predictor variables like the P/E ratio, the dividend yield, the default spread,
and the consumption-wealth ratio (CAY). Moreover, combining the variance risk premium with the P/E
ratio results in an R2 for the quarterly returns of more than twenty-five percent. The results depend
crucially on the use of “model free”, as opposed to standard Black-Scholes, implied variances, and
realized variances constructed from high-frequency intraday, as opposed to daily, data. Our findings
suggest that temporal variation in both risk-aversion and volatility-risk play an important role in
determining stock market returns.
3. “Copula-based Semiparametric Quantile Autoregression”
Xiaohong CHEN (Yale University, USA), Roger Koenker (University of Illinois Champaign, USA) and
Zhijie Xiao (Boston College, USA)
Abstract:
We study semiparametric estimation of conditional quantiles for nonlinear time series models. We model
serial dependence using copula functions that have direct quantile representations, thus the conditional
Value-at-Risk (VaR, quantiles) can be estimated based a quantile autoregression. The proposed
estimator is semiparametric in the sense that we characterize the serial dependence in data using
parametric copula functions but model the invariant (marginal) distribution nonparametrically.
4. “International Market Links and Realized Volatility Transmission”
Valentina CORRADI (Warwick, UK), Walter Distaso (Tanaka, London, UK) and Marcelo Fernades
(Queen Mary University of London, UK)
Abstract:
The analysis of volatility transmission is not only essential to understand the information flow process,
but also helps identifying the appropriate multivariate model for estimating and predicting volatility. In
this paper, we develop formal statistical tools for testing conditional independence and noncausality that
are suitable for checking for volatility spillovers in asset prices. We take a different route from the
previous papers in the literature in that we make no parametric assumption on the stochastic volatility
processes and on the form that they interrelate. In particular, our testing procedure is in two steps. In
the first stage, we estimate the daily volatilities of the assets under consideration by means of realized
measures under the mild assumption that asset prices follow continuous-time jump-diffusion processes
with stochastic volatility. Microstructure effects are taken into account too. In the second step, we test
for conditional independence by checking whether the corresponding density restrictions hold for the
nonparametric estimates of the volatility distributions. The asymptotic results that we derive entail some
interesting contributions to the nonparametric literature by clarifying the impact of the realized volatility
estimation error. We also contribute to the volatility transmission literature by empirically investigating
volatility spillovers between the stock markets in China, Japan, and US.
5. “Modelling and Forecasting Intraday Volatility with Unobserved Component Structures"
Gabriele FIORENTINI (Florence University, Italy) and Christian Macaro
Abstract:
We propose a model for intraday return volatility based on the information brought by tick by tick
quotes. The volatility is decomposed into the product of unobserved stochastic components that typically
reflect the short term, the daily and persistent, and the intraday "seasonal" variations. The models for
the components are identified by the so-called canonical decomposition and estimated with the WienerKolmogorov filter. Alternatively we formulate an equivalent state space representation that can be
estimated with the diffuse Kalman filter. We also augment the model with weakly exogenous variables to
take into account the effects of overnight returns, day of the week, and outliers. In the empirical
application we consider four equities traded at the New York Stock Exchange. The forecasting
performance of our model is evaluated by means of an extensive out of sample forecasting exercise.
6. “Dependence Structure and Extreme Comovements in International Equity and Bond Markets with
Portfolio Diversification Effects”
Rene GARCIA (Universite de Montreal, Canada, and Nice University, France)
Abstract:
Equity returns are more dependent in bear markets than in bull markets. This phenomenon known as
asymmetric dependence is well documented. Previous studies have argued that a multivariate GARCH
model or a regime switching (RS) model based on normal innovations could reproduce this asymmetric
extreme dependence. We show analytically that it cannot be the case. We propose an alternative model
that allows tail dependence for lower returns and keeps tail independence for upper returns. This model
is applied to international equity and bond markets to investigate their dependence structure. It includes
one normal regime in which dependence is symmetric and a second regime characterized by asymmetric
dependence. Empirical results show that the dependence between equities and bonds is low even in the
same country, while the dependence between international assets of the same type is large in both
regimes. The cross-country dependence is especially large in the asymmetric regime. Empirical
phenomena such as home bias investment and flight to safety are amplified by asymmetric dependence
through coskewness.
7. “When is a Copula Constant? A Test for Changing Relationships”
Fabio Busetti (Bank of Italy) and Andrew HARVEY (Faculty of Economics, Cambridge University)
Abstract:
A copula defines the probability that the observations from two time series are both below a given
quantile. It is proposed that stationarity tests constructed from indicator variables be used to test
against the hypothesis that the copula is changing over time. Tests associated with different quantiles
may point to changes in different parts of the copula, with the lower quantiles being of particular interest
in financial applications concerned with risk. Tests located at the median provide an overall test of a
changing relationship. The properties of various tests are compared and it is shown that they are still
effective if pre-filtering is carried out to correct for changing volatility or, more generally, changing
quantiles. Applying the tests to data on IBM and General Motors stock returns indicates that the
relationship is not constant over time.
8. “Testing Dynamics in Conditional Asymmetry. A Residual-Based Approach”
Philippe Lambert, Sébatien LAURENT (FUNDP and CORE) and David Veredas
Abstract:
We propose parametric and non-parametric residual-based tests ford ynamics in conditional asymmetry.
Estimation is done under the null hypothesis of constant asymmetry of the innovations and, in a second
step, the tests are performed either through a parametric model or a nonparametric method (runs). The
working distribution is assumed to fall into the class of skewed distributions of Fernandez and Steel
(1998). Asymmetry is measured by the ratio between the probabilities of being larger and smaller than
the mode. The asymptotic distribution of the tests is derived by incorporating the uncertainty of the
estimated parameters in the first step . A Monte Carlo study shows that neglecting this uncertainty
severely biases the tests. An empirical application on a basket of daily returns of bonds, indexes and
stocks reveals that financial data often present dynamics in the conditional skewness.
9. “Estimation of a Semiparametric Multivariate Multiplicative Volatility Model”
Christian Hafner (UCL) and Oliver LINTON (London School of Economics, UK)
Abstract:
We propose a multivariate generalization of the multiplicative volatility model of Engle and Rangel
(2006), which has a nonparametric long run component and a unit multivariate GARCH short run
dynamic component. We suggest various estimation procedures for the parametric and nonparametric
components, and derive the asymptotic properties thereof. We obtain the semiparametric efficiency
bound for the parametric part. We apply our method to exchange rate data.
10. “Generalized Affine Models”
Nour MEDDAHI (Tanaka Business School, London, UK) and Bruo Feunou
Abstract:
Affine models are very popular in modeling financial time series as they allow for analytical calculation of
prices of financial derivatives like treasury bonds and options. The main property of affine models is that
the conditional cumulant function, defined as the logarithmic of the conditional characteristic function, is
affine in the state variable. Consequently, an affine model is Markovian, like an autoregressive process,
which is an empirical limitation. The paper generalizes affine models by adding in the current conditional
cumulant function the past conditional cumulant function. Hence, generalized affine models are nonMarkovian, such as ARMA and GARCH processes, allowing one to disentangle the short term and longrun dynamics of the process. Importantly, the new model keeps the tractability of prices of financial
derivatives. This paper studies the statistical properties of the new model, derives its conditional and
unconditional moments, as well as the conditional cumulant function of future aggregated values of the
state variable which is critical for pricing financial derivatives. It derives the analytical formulas of the
term structure of interest rates and option prices. Different estimating methods are discussed (MLE,
QML, GMM, and characteristic function based estimation methods). Three empirical applications
developed in companion papers are
presented. The first one based on Feunou (2007) presents a no-arbitrage VARMA term structure model
with macroeconomic variables and shows the empirical importance of the inclusion of the MA
component. The second application based on Feunou and Meddahi (2007a) models jointly the highfrequency realized variance and the daily asset return and provides the term structure of risk measures
such as the Value-at-Risk, and highlights the powerful use of generalized affine models. The third
application based on Feunou, Christoffersen, Jacobs and Meddahi (2007) uses the model developed in
Feunou and Meddahi (2007a) to price options theoretically and empirically.
11. "Modelling Volatilities and Conditional Correlations in Futures Markets with a Multivariate
Distribution"
Bahram PESARAN (Wadhwani Asset Management, LLP, London UK) and M. Hashem Pesaran
(Cambridge University, UK)
Abstract:
This paper considers a multivariate t version of the Gaussian dynamic conditional correlation (DCC)
model proposed by Engle (2002), and suggests the use of devolatized returns computed as returns
standardized by realized volatilities rather than by GARCH type volatility estimates. The t-DCC
estimation procedure is applied to a portfolio of daily returns on currency futures, government bonds
and equity index futures. The results strongly reject the normal-DCC model in favour of a t-DCC
specification. The t-DCC model also passes a number of VaR diagnostic tests over an evaluation sample.
The estimation results suggest a general trend towards a lower level of return volatility, accompanied by
a rising trend in conditional cross correlations in most markets; possibly reflecting the advent of euro in
1999 and increased interdependence of financial markets.
12. "Fitting and Testing Vast Dimensional Time-Varying Covariance Models"
Neil SHEPHARD (Oxford University, UK)
Abstract:
Building models for high dimensional portfolios is important in risk management and asset allocation.
Here we propose a novel way of estimating models of time-varying covariances that overcome some of
the computational problems which have troubled existing methods when applied to 1,000s of assets.
The theory of this new strategy is developed in some detail, allowing formal hypothesis testing to be
carried out on these models. Simulations are used to explore the performance of this inference strategy
while empirical examples are reported which show the strength of this method.
13. “The Joint Behaviour of Credit Spreads, Stock Options and Equity Returns when Investors Disagree”
Andrea Buraschi (Tanaka Business School, Imperial College, London, UK), Fabio TROJANI (St. Gallen
University, CH) and Andrea Vedolin.
Abstract:
In an economy in which investors have heterogenous beliefs on a firm’s future cash flows, we derive the
implications for the joint behavior of credit spreads, stock returns, and option implied volatilities. Beliefs
disagreement helps to explain several empirical facts documented in the literature. First, beliefs
heterogeneity impacts on the market price of risk and the volatility of the pricing kernel in a way that
increases corporate credit spreads to more realistic levels. Second, it generates a positive co–movement
between credit spreads and option-implied volatilities. Third, the endogenous interaction between option
implied volatility skew and leverage in our model gives a structural explanation for the inverted volatility
skews of some single-stock options. Fourth, the model also helps to explain why the delta of call (put)
options are often found to be negative (positive) and non monotonic in credit spreads. In the empirical
analysis, we match four data sets of firm–specific information on professional earning forecasts,
balance-sheet data, corporate bond spreads, and individual option prices. We test the main model
predictions and find that disagreement among investors consistently impacts on credit spreads, stock
returns, and the volatility smile of individual options, even after controlling for other control variables.
14. “Multivariate GARCH Model for the Non-Normal Behaviour of Financial Assets. Alternative classes of
DCC models”.
Juan Cajigas (Cass Business School, London, UK) and Giovanni URGA (Cass Business School, London,
UK and University of Bergamo, Italy)
Abstract:
In this paper we provide an evaluation of the class of DCC models proposed in the financial econometrics
literature since the seminal contribution by Engle (2002). We a propose to estimate multivariate GARCH
processes and a class of dynamic conditional correlation (DCC) models assuming that the n-dimensional
returns series follow an asymmetric multivariate Laplace (AML) distribution. This multivariate distribution
is able to capture leptokurtosis and asymmetry which characterize returns from financial assets. It
preserves, under general conditions, desirable properties such as finiteness of moments and stability
under geometric summation. We provide conditions for the consistency of parameter estimates in
multivariate GARCH models obtained by MLE assuming an AML law for the distribution of standardised
residuals and we verify that these conditions are valid for our AGDCC model. Finally, we prove strict
stationarity of the AGDDCC model. We illustrate the methodology by fitting a sample of 21 FTSE AllWorld stock indices and 13 bond return indices. We provide clear evidence that in our data set the
asymmetric generalised dynamic conditional correlation (AGDCC)-MGARCH model with AML distribution
of innovations overwhelmingly outperforms the class of DCC-MGARCH models that assume normality of
innovations
15. "Estimating Conditional Quantiles in GARCH Models"
Zhijie XIAO (Boston College, USA)
Abstract:
Conditional quantile is an essential ingredient in various risk measures, and the GARCH process has
proven to be highly successful in modelling financial data. In this paper, we study estimation of
conditional quantiles for GARCH Models using quantile regressions. Quantile regression estimation of
GARCH models is highly nonlinear. In this paper, we propose a simple and effective two-step approach
of quantile regression estimation for linear GARCH time series: In the first step, we propose a time
series sieve quantile regression approximation for the GARCH model; a second stage estimation for the
GARCH model is then constructed based on the preliminary estimators. Asymptotic property of time
series sieve quantile regression and quantile regression estimation with generated regressors are
studied. These results are of independent interest and can be applied to other quantile regression
applications. Monte Carlo results indicate that the proposed estimation method outperforms over
existing quantile estimation methods.