Return and volatility linkages between the S&P 500 and emerging stock markets in Eastern Europe

The aim of this thesis is to research mean return spillovers as well as volatility spillovers from the S&P 500 stock index in the USA to selected stock markets in the emerging economies in Eastern Europe between 2002 and 2014. The sample period has been divided into smaller subsamples, which enables taking different market conditions as well as the unification of the World’s capital markets during the financial crisis into account. Bivariate VAR(1) models are used to analyze the mean return spillovers while the volatility linkages are analyzed through the use of bivariate BEKK-GARCH(1,1) models. The results show both constant volatility pooling within the S&P 500 as well as some statistically significant spillovers of both return and volatility from the S&P 500 to the Eastern European emerging stock markets. Moreover, some of the results indicate that the volatility spillovers have increased as time has passed, indicating unification of global stock markets.

Margin requirements and volatility : evidence from Canadian stocks

Margin policy is used by regulators for the purpose of inhibiting exceSSIve volatility and stabilizing the stock market in the long run. The effect of this policy on the stock market is widely tested empirically. However, most prior studies are limited in the sense that they investigate the margin requirement for the overall stock market rather than for individual stocks, and the time periods examined are confined to the pre-1974 period as no change in the margin requirement occurred post-1974 in the U.S. This thesis intends to address the above limitations by providing a direct examination of the effect of margin requirement on return, volume, and volatility of individual companies and by using more recent data in the Canadian stock market. Using the methodologies of variance ratio test and event study with conditional volatility (EGARCH) model, we find no convincing evidence that change in margin requirement affects subsequent stock return volatility. We also find similar results for returns and trading volume. These empirical findings lead us to conclude that the use of margin policy by regulators fails to achieve the goal of inhibiting speculating activities and stabilizing volatility.

The information content of Canadian implied volatility indexes

For predicting future volatility, empirical studies find mixed results regarding two issues: (1) whether model free implied volatility has more information content than Black-Scholes model-based implied volatility; (2) whether implied volatility outperforms historical volatilities. In this thesis, we address these two issues using the Canadian financial data. First, we examine the information content and forecasting power between VIXC - a model free implied volatility, and MVX - a model-based implied volatility. The GARCH in-sample test indicates that VIXC subsumes all information that is reflected in MVX. The out-of-sample examination indicates that VIXC is superior to MVX for predicting the next 1-, 5-, 10-, and 22-trading days' realized volatility. Second, we investigate the predictive power between VIXC and alternative volatility forecasts derived from historical index prices. We find that for time horizons lesser than 10-trading days, VIXC provides more accurate forecasts. However, for longer time horizons, the historical volatilities, particularly the random walk, provide better forecasts. We conclude that VIXC cannot incorporate all information contained in historical index prices for predicting future volatility.

Volume-Synchronized Probability of Informed Trading (VPIN), Market Volatility, and High-Frequency Liquidity

We assess the predictive ability of three VPIN metrics on the basis of two highly volatile market events of China, and examine the association between VPIN and toxic-induced volatility through conditional probability analysis and multiple regression. We examine the dynamic relationship on VPIN and high-frequency liquidity using Vector Auto-Regression models, Granger Causality tests, and impulse response analysis. Our results suggest that Bulk Volume VPIN has the best risk-warning effect among major VPIN metrics. VPIN has a positive association with market volatility induced by toxic information flow. Most importantly, we document a positive feedback effect between VPIN and high-frequency liquidity, where a negative liquidity shock boosts up VPIN, which, in turn, leads to further liquidity drain. Our study provides empirical evidence that reflects an intrinsic game between informed traders and market makers when facing toxic information in the high-frequency trading world.

An Eigenfunction Approach for Volatility Modeling.

In this paper, we introduce a new approach for volatility modeling in discrete and continuous time. We follow the stochastic volatility literature by assuming that the variance is a function of a state variable. However, instead of assuming that the loading function is ad hoc (e.g., exponential or affine), we assume that it is a linear combination of the eigenfunctions of the conditional expectation (resp. infinitesimal generator) operator associated to the state variable in discrete (resp. continuous) time. Special examples are the popular log-normal and square-root models where the eigenfunctions are the Hermite and Laguerre polynomials respectively. The eigenfunction approach has at least six advantages: i) it is general since any square integrable function may be written as a linear combination of the eigenfunctions; ii) the orthogonality of the eigenfunctions leads to the traditional interpretations of the linear principal components analysis; iii) the implied dynamics of the variance and squared return processes are ARMA and, hence, simple for forecasting and inference purposes; (iv) more importantly, this generates fat tails for the variance and returns processes; v) in contrast to popular models, the variance of the variance is a flexible function of the variance; vi) these models are closed under temporal aggregation.

Aggregations and Marginalization of GARCH and Stochastic Volatility Models

The GARCH and Stochastic Volatility paradigms are often brought into conflict as two competitive views of the appropriate conditional variance concept : conditional variance given past values of the same series or conditional variance given a larger past information (including possibly unobservable state variables). The main thesis of this paper is that, since in general the econometrician has no idea about something like a structural level of disaggregation, a well-written volatility model should be specified in such a way that one is always allowed to reduce the information set without invalidating the model. To this respect, the debate between observable past information (in the GARCH spirit) versus unobservable conditioning information (in the state-space spirit) is irrelevant. In this paper, we stress a square-root autoregressive stochastic volatility (SR-SARV) model which remains true to the GARCH paradigm of ARMA dynamics for squared innovations but weakens the GARCH structure in order to obtain required robustness properties with respect to various kinds of aggregation. It is shown that the lack of robustness of the usual GARCH setting is due to two very restrictive assumptions : perfect linear correlation between squared innovations and conditional variance on the one hand and linear relationship between the conditional variance of the future conditional variance and the squared conditional variance on the other hand. By relaxing these assumptions, thanks to a state-space setting, we obtain aggregation results without renouncing to the conditional variance concept (and related leverage effects), as it is the case for the recently suggested weak GARCH model which gets aggregation results by replacing conditional expectations by linear projections on symmetric past innovations. Moreover, unlike the weak GARCH literature, we are able to define multivariate models, including higher order dynamics and risk premiums (in the spirit of GARCH (p,p) and GARCH in mean) and to derive conditional moment restrictions well suited for statistical inference. Finally, we are able to characterize the exact relationships between our SR-SARV models (including higher order dynamics, leverage effect and in-mean effect), usual GARCH models and continuous time stochastic volatility models, so that previous results about aggregation of weak GARCH and continuous time GARCH modeling can be recovered in our framework.

Jumps in the Volatility of Financial Markets.

Recent work suggests that the conditional variance of financial returns may exhibit sudden jumps. This paper extends a non-parametric procedure to detect discontinuities in otherwise continuous functions of a random variable developed by Delgado and Hidalgo (1996) to higher conditional moments, in particular the conditional variance. Simulation results show that the procedure provides reasonable estimates of the number and location of jumps. This procedure detects several jumps in the conditional variance of daily returns on the S&P 500 index.

Correcting the Errors : A Note on Volatility Forecast Evaluation Based on High-Frequency Data and Realized Volatilities

This note develops general model-free adjustment procedures for the calculation of unbiased volatility loss functions based on practically feasible realized volatility benchmarks. The procedures, which exploit the recent asymptotic distributional results in Barndorff-Nielsen and Shephard (2002a), are both easy to implement and highly accurate in empirically realistic situations. On properly accounting for the measurement errors in the volatility forecast evaluations reported in Andersen, Bollerslev, Diebold and Labys (2003), the adjustments result in markedly higher estimates for the true degree of return-volatility predictability.

Arbitrage-Based Pricing when Volatility is Stochastic.

The paper investigates the pricing of derivative securities with calendar-time maturities.

Stochastic Volatility.

This paper prepared for the Handbook of Statistics (Vol.14: Statistical Methods in Finance), surveys the subject of stochastic volatility. the following subjects are covered: volatility in financial markets (instantaneous volatility of asset returns, implied volatilities in option prices and related stylized facts), statistical modelling in discrete and continuous time and, finally, statistical inference (methods of moments, quasi-maximum likelihood, likelihood-based and bayesian methods and indirect inference).