ARCH and GARCH models vs. martingale volatility of finance market returns

ARCH and GARCH models assume either i.i.d. or ‘white noise’ as is usual in regression analysis, while also assuming memory in a conditional mean square fluctuation with stationary increments. We will show that ARCH/GARCH is inconsistent with uncorrelated increments, violating the i.i.d. and ‘white’ assumptions, and violating finance data and the efficient market hypothesis as well.     

Bayesian Statistical Computations of Nonlinear Financial Time Series Models: A Survey with Illustrations

A survey of Bayesian statistical computations of quadratureformula, Laplace approximation, and Markov Chain Monte Carlo algorithms ispresentedand their applications to nonlinear financial time series models arediscussed.     

上海原油期货与国际原油期货:联动机制和溢出效应

建立VECM—GARCH—BEKK—T模型,分析了上海原油期货价格与WTI、布伦特两大国际基准油价格之间的传导效应、均值溢出效应、波动溢出效应、BEKK交叉效应以及杠杆效应。研究发现,上海、WTI和布伦特原油期货三个市场存在显著的均值溢出和波动溢出效应。其中,上海原油期货上市重构了WTI和布伦特原油期货两个市场的均衡关系、主导影响因素、影响期限以及波动溢出效应;上海原油期货与国际油价有机联动,对WTI的正向影响要大于对布伦特的影响,但WTI、布伦特对上海的影响依然占主导地位。此外,短期内,当期上海原油期货价格与历史WTI和上海原油期货价格波动联系显著为正,而与历史布伦特原油期货价格则显著为负。因此,需要在持续提高上海原油期货参与者数量、提高国际参与度和认可度、完善原油期货区间波段管理机制、提升原油期货交易量、加快人民币国际化进程等方面努力。     

Varying the VaR for unconditional and conditional environments

Accurate forecasting of risk is the key to successful risk management techniques. Using the largest stock index futures from 12 European bourses, this paper presents VaR measures based on their unconditional and conditional distributions for single and multi-period settings. These measures underpinned by extreme value theory are statistically robust explicitly allowing for fat-tailed densities. Conditional tail estimates accounting for volatility clustering are obtained by adjusting the unconditional extreme value procedure with GARCH filtered returns. The conditional modelling results in iid returns allowing for the use of a simple and efficient multi-period extreme value scaling law. The paper examines the properties of these distinct conditional and unconditional trading models. The paper finds that the biases inherent in unconditional single and multi-period estimates assuming normality extend to the conditional setting.     

Price transmission and volatility spillovers in Asian rice markets: Evidence from MGARCH and panel GARCH models

ABSTRACT

This article examines world rice price transmission and volatility spillovers across six major Asian rice markets over the period 2005-13. In addition to the conventional GARCH models, we use a panel GARCH framework to estimate the spillover effects along with the consideration of heterogeneity and interdependence among countries. Empirical results suggest that changes in the world rice price affected not only the price levels of domestic rice markets but also their conditional variances. Moreover, interdependence across rice markets contributed to a strong spillover of a price shock in one country to another within the region.     

The information content of implied volatility in developed versus developing FX markets

This article predicts the daily movement of monthly foreign exchange (FX) rate volatility using a linear combination of a time-series model and implied volatilities from options. The focus is on analysing the FX volatilities in three developing economies (the Brazilian real (BRL), the Indian rupee (INR) and the Russian ruble (RUB)) against the US dollar (USD). The empirical exercise utilizes two time-series models, mixed data sampling (MIDAS) and GARCH. The analysis indicates that for both developed and developing economies the predictive power of MIDAS and that of GARCH is comparable. Further on in this article, we will ascertain whether the relationship between realized and implied volatility is fundamentally different in the case of developing economies from that among developed economies. Thus, we compare the pairs USD/BRL, USD/INR and USD/RUB against EURO/USD and USD/Japanese yen to determine the information content and predictive power of implied volatilities. Plots of the MIDAS coefficients show that the volatility is more persistent in developing economies than in developed economies.     

The relationship between stock returns and volatility in international stock markets

This study examines the relationship between expected stock returns and volatility in the 12 largest international stock markets during January 1980 to December 2001. Consistent with most previous studies, we find a positive but insignificant relationship during the sample period for the majority of the markets based on parametric EGARCH-M models. However, using a flexible semiparametric specification of conditional variance, we find evidence of a significant negative relationship between expected returns and volatility in 6 out of the 12 markets. The results lend some support to the recent claim [Bekaert, G., Wu, G., 2000. Asymmetric volatility and risk in equity markets. Review of Financial Studies 13, 1–42; Whitelaw, R., 2000. Stock market risk and return: an empirical equilibrium approach. Review of Financial Studies 13, 521–547] that stock market returns are negatively correlated with stock market volatility.     

Volatility Relationship between Crude Oil and Petroleum Products

This paper utilizes calculated historical volatility and GARCH models to compare the historical price volatility behavior of crude oil, motor gasoline and heating oil in U.S. markets since 1990. We incorporate a shift variable in the GARCH/TARCH models to capture the response of price volatility to a change in OPEC’s pricing behavior. This study has three major conclusions. First, there was an increase in volatility as a result of a structural shift to higher crude oil prices after April 1999. Second, volatility shocks from current news are not important since GARCH effects dominate ARCH effects in the variance equation. Third, persistence of volatility in all commodity markets is quite transitory, with half-lives normally being a few weeks.

MACROECONOMIC UNCERTAINTY AND CONDITIONAL STOCK MARKET VOLATILITY IN SOUTH AFRICA*

This paper analyses how systematic risk emanating from the macroeconomy is transmitted into stock market volatility using augmented autoregressive Generalised Autoregressive Conditional Heteroscedastic (AR‐GARCH) and vector autoregression (VAR) models. Also examined is whether the relationship between the two is bidirectional. By imposing dummies for the 1997‐1998 Asian and the 2007‐2009 sub‐prime financial crises, the study further analyses whether financial crises affect the relationship between macroeconomic uncertainty and stock market volatility. The findings show that macroeconomic uncertainty significantly influences stock market volatility. Although volatilities in inflation, the gold price and the oil price seem to play a role, it is found that volatility in short‐term interest rates and exchange rates are the most important, suggesting that South African domestic financial markets are increasingly becoming interdependent. Finally, the results show that financial crises increase volatility in the stock market and in most macroeconomic variables, and, by so doing, strengthen the effects of changes in macroeconomic variables on the stock market.     

Valuation of VIX and target volatility options with affine GARCH models

In this paper we propose semiclosed-form solutions, subject to an inversion of the Fourier transform, for the price of VIX options and target volatility options under affine GARCH models based on Gaussian and Inverse Gaussian distributions. We illustrate the advantage of the proposed analytic expressions by comparing them with those obtained from benchmark Monte–Carlo simulations. The empirical performance of the two affine GARCH models is tested using different calibration exercises based on historical returns and market quotes on VIX and SPX options.