"Fat Tails and Asymmetry in Financial Volatility Models"

Although the GARCH model has been quite successful in capturing important empirical aspects of financial data, particularly for the symmetric effects of volatility, it has had far less success in capturing the effects of extreme observations, outliers and skewness in returns. This paper examines the GARCH model under various non-normal error distributions in order to evaluate skewness and leptokurtosis. The empirical results show that GARCH models estimated using asymmetric leptokurtic distributions are superior to their counterparts estimated under normality, in terms of: (i) capturing skewness and leptokurtosis; (ii) the maximized log-likelihood values; and (iii) isolating the ARCH and GARCH parameter estimates from the adverse effects of outliers. Overall, the flexible asymmetric Student-t distribution performs best in terms of capturing the non-normal aspects of the data.

Asymmetry in Volatility: A Comparison of Developed and Transition Stock Markets

ARCH modelling framework of Engle (1982) and its GARCH generalization of Bollerslev (1986) gave a huge impetus to econometric model building in the field of financial time series with time-varying variance. The main idea of the models was to describe the most typical features of capital markets like volatility clustering, excess kurtosis and fat tails. As empirical evidence shows asymmetry is also a prominent feature of stock market returns volatility. The reaction of risk if stock returns go off the long run trajectory is different in case of positive and negative market news. Thus it is indispensable to employ asymmetric models being a modification of a traditional GARCH. In the paper we used an approach of Engle and Ng (1993) to test for asymmetric effects in stock indices of developed and Central European stock markets.asymmetry, volatility, stock market, transition

Value-at-Risk and Expected Shortfall when there is long range dependence.

Empirical studies have shown that a large number of financial asset returns exhibit fat tails and are often characterized by volatility clustering and asymmetry. Also revealed as a stylized fact is Long memory or long range dependence in market volatility, with significant impact on pricing and forecasting of market volatility. The implication is that models that accomodate long memory hold the promise of improved long-run volatility forecast as well as accurate pricing of long-term contracts. On the other hand, recent focus is on whether long memory can affect the measurement of market risk in the context of Value-at- Risk (V aR). In this paper, we evaluate the Value-at-Risk (V aR) and Expected Shortfall (ESF) in financial markets under such conditions. We examine one equity portfolio, the British FTSE100 and three stocks of the German DAX index portfolio (Bayer, Siemens and Volkswagen). Classical V aR estimation methodology such as exponential moving average (EMA) as well as extension to cases where long memory is an inherent characteristics of the system are investigated. In particular, we estimate two long memory models, the Fractional Integrated Asymmetric Power-ARCH and the Hyperbolic-GARCH with different error distribution assumptions. Our results show that models that account for asymmetries in the volatility specifications as well as fractional integrated parametrization of the volatility process, perform better in predicting the one-step as well as five-step ahead V aR and ESF for short and long positions than short memory models. This suggests that for proper risk valuation of options, the degree of persistence should be investigated and appropriate models that incorporate the existence of such characteristic be taken into account.Backtesting, Value-at-Risk, Expected Shortfall, Long Memory, Fractional Integrated Volatility Models

The Nature of Alpha

We suggest an empirical model of investment strategy returns which elucidates the importance of non-Gaussian features, such as time-varying volatility, asymmetry and fat tails, in explaining the level of expected returns. Estimating the model on the (former) Lehman Brothers Hedge Fund Index data, we demonstrate that the volatility compensation is a significant component of the expected returns for most strategy styles, suggesting that many of these strategies should be thought of as being `short vol'. We present some fundamental and technical reasons why this should indeed be the case, and suggest explanation for exception cases exhibiting `long vol' characteristics. We conclude by drawing some lessons for hedge fund portfolio construction.Comment: 22 pages, 5 figures, 3 table

Econometric Analysis of Financial Derivatives

__Abstract__ One of the fastest growing areas in empirical finance, and also one of the least rigorously analyzed, especially from a financial econometrics perspective, is the econometric analysis of financial derivatives, which are typically complicated and difficult to analyze. The purpose of this special issue of the journal on “Econometric Analysis of Financial Derivatives” is to highlight several areas of research by leading academics in which novel econometric, financial econometric, mathematical finance and empirical finance methods have contributed significantly to the econometric analysis of financial derivatives, including market-based estimation of stochastic volatility models, the fine structure of equity-index option dynamics, leverage and feedback effects in multifactor Wishart stochastic volatility for option pricing, option pricing with non-Gaussian scaling and infinite-state switching volatility, stock return and cash flow predictability: the role of volatility risk, the long and the short of the risk-return trade-off, What’s beneath the surface? option pricing with multifrequency latent states, bootstrap score tests for fractional integration in heteroskedastic ARFIMA models, with an application to price dynamics in commodity spot and futures markets, a stochastic dominance approach to financial risk management strategies, empirical evidence on the importance of aggregation, asymmetry, and jumps for volatility prediction, non-linear dynamic model of the variance risk premium, pricing with finite dimensional dependence, quanto option pricing in the presence of fat tails and asymmetric dependence, smile from the past: a general option pricing framework with multiple volatility and leverage components, COMFORT: A common market factor non-Gaussian returns model, divided governments and futures prices, and model-based pricing for financial derivative

Econometric Analysis of Financial Derivatives: An Overview

One of the fastest growing areas in empirical finance, and also one of the least rigorously analyzed, especially from a financial econometrics perspective, is the econometric analysis of financial derivatives, which are typically complicated and difficult to analyze. The purpose of this special issue of the journal on “Econometric Analysis of Financial Derivatives” is to highlight several areas of research by leading academics in which novel econometric, financial econometric, mathematical finance and empirical finance methods have contributed significantly to the econometric analysis of financial derivatives, including market-based estimation of stochastic volatility models, the fine structure of equity-index option dynamics, leverage and feedback effects in multifactor Wishart stochastic volatility for option pricing, option pricing with non-Gaussian scaling and infinite-state switching volatility, stock return and cash flow predictability: the role of volatility risk, the long and the short of the risk-return trade-off, What’s beneath the surface? option pricing with multifrequency latent states, bootstrap score tests for fractional integration in heteroskedastic ARFIMA models, with an application to price dynamics in commodity spot and futures markets, a stochastic dominance approach to financial risk management strategies, empirical evidence on the importance of aggregation, asymmetry, and jumps for volatility prediction, non-linear dynamic model of the variance risk premium, pricing with finite dimensional dependence, quanto option pricing in the presence of fat tails and asymmetric dependence, smile from the past: a general option pricing framework with multiple volatility and leverage components, COMFORT: A common market factor non-Gaussian returns model, divided governments and futures prices, and model-based pricing for financial derivative

The time-varying asymmetry of exchange rate returns : a stochastic volatility - stochastic skewness model

While the time-varying volatility of financial returns has been extensively modelled, most existing stochastic volatility models either assume a constant degree of return shock asymmetry or impose symmetric model innovations. However, accounting for time-varying asymmetry as a measure of crash risk is important for both investors and policy makers. This paper extends a standard stochastic volatility model to allow for time-varying skewness of the return innovations. We estimate the model by extensions of traditional Markov Chain Monte Carlo (MCMC) methods for stochastic volatility models. When applying this model to the returns of four major exchange rates, skewness is found to vary substantially over time. In addition, stochastic skewness can help to improve forecasts of risk measures. Finally, the results support a potential link between carry trading and crash risk