Detecting and modeling changing volatility in the copper futures market

Copper futures returns are characterized by negative skewness and excess kurtosis. Research has not yet examined this nonnormality, which contributes to their volatility. To date little attention has been paid to the modeling of these series. Therefore, the purpose of this paper is to (i) detect alternating subperiods of volatility by using a method that uses an iterated cumulative sum of squares (ICSS) algorithm to identify breakpoints in the series; and (ii) compare the ability of five models (the random walk, GARCH, EGARCH, AGARCH, and the GJR model) to capture the volatility within each ICSS identified subperiod. These tests were applied to two copper futures series (open to close and close to close prices). Results indicate that the ranking (in terms of the root mean square error) is similar for both series. That is, the GARCH or EGARCH model rank first and second, depending on the series, followed by the GJR model. AGARCH and the random walk models perform poorly.© 1999 John Wiley & Sons, Inc. Jrl Fut Mark 19: 79–100, 1999     

Switching asymmetric GARCH and options on a volatility index

Few proposed types of derivative securities have attracted as much attention and interest as option contracts on volatility. Grunbichler and Longstaff (1996) is the only study that proposes a model to value options written on a volatility index. Their model, which is based on modeling volatility as a GARCH process, does not take into account the switching regime and asymmetry properties of volatility. We show that the Grunbichler and Longstaff (1996) model underprices a three‐month option by about 10%. A Switching Regime Asymmetric GARCH is used to model the generating process of security returns. The comparison between the switching regime model and the traditional uni‐regime model among GARCH, EGARCH, and GJR‐GARCH demonstrates that a switching regime EGARCH model fits the data best. Next, the values of European call options written on a volatility index are computed using Monte Carlo integration. When comparing the values of the option based on the Switching Regime Asymmetric GARCH model and the traditional GARCH specification, it is found that the option values obtained from the different processes are very different. This clearly shows that the Grunbichler‐Longstaff model is too stylized to be used in pricing derivatives on a volatility index. © 2004 Wiley Periodicals, Inc. Jrl Fut Mark 24:251–282, 2004     

The information content of implied volatility: Evidence from Australia

This study develops an implied volatility index for the Australian stock market, termed as the AVX, and assesses its information content. The AVX is constructed using S&P/ASX 200 index options with a constant time‐to‐maturity of three months. It is observed that the AVX has a significant negative and asymmetric relationship with S&P/ASX 200 returns. When evaluating the forecasting power of the AVX for future stock market volatility, it is found that the AVX contains important information both in‐sample and out‐of‐sample. In‐sample, the AVX significantly improves the fit of a GJR‐GARCH(1, 1) model. Out‐of‐sample, the AVX significantly outperforms the RiskMetrics approach and the GJR‐GARCH(1, 1) model, with its highest forecasting power at the one‐month forecasting horizon. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 30:134–155, 2010     

Testing mean reversion in financial market volatility: Evidence from S&P 500 index futures

This article presents a comprehensive study of continuous time GARCH (generalized autoregressive conditional heteroskedastic) modeling with the thintailed normal and the fat‐tailed Student's‐t and generalized error distributions (GED). The study measures the degree of mean reversion in financial market volatility based on the relationship between discrete‐time GARCH and continuoustime diffusion models. The convergence results based on the aforementioned distribution functions are shown to have similar implications for testing mean reversion in stochastic volatility. Alternative models are compared in terms of their ability to capture mean‐reverting behavior of futures market volatility. The empirical evidence obtained from the S&P 500 index futures indicates that the conditional variance, log‐variance, and standard deviation of futures returns are pulled back to some long‐run average level over time. The study also compares the performance of alternative GARCH models with normal, Student's‐ t, and GED density in terms of their power to predict one‐day‐ahead realized volatility of index futures returns and provides some implications for pricing futures options. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:1–33, 2008     

中国线材期货价格指数波动率预测能力分析

利用上海期货交易所线材期货15分钟高频价格数据构造已实现波动率估计序列,并以此作为参考标准,运用6种损失函数以及Diebold-Mariano检验法检验4类不同波动率模型对线材期货价格波动的样本外预测能力,显示,中国线材期货市场,基于高频数据的GJR(1,1)模型具有最为出色的波动率预测能力,而在某些损失函数标准下,HYGARCH(1,d,1)与GARCH(1,1)模型也体现出了较好的波动率预测能力。     

Implied volatility forecasts in the grains complex

This article finds that the implied volatilities of corn, soybean, and wheat futures options 4 weeks before option expiration have significant predictive power for the underlying futures contract return volatilities through option expiration from January 1988 through September 1999. These implied volatilities also encompass the information in out‐of‐sample seasonal Glosten, Jagannathan, and Runkle (GJR;1993) volatility forecasts. Evidence also demonstrates that when corn‐implied volatility rises relative to out‐of‐sample seasonal GJR volatility forecasts, implied volatility substantially overpredicts realized volatility. However, simulations of trading rules that involve selling corn option straddles when corn‐implied volatility is high relative to out‐of‐sample GJR volatility forecasts indicate that none of the trading rules would have been significantly profitable. This finding suggests that these options are not necessarily overpriced. © 2002 Wiley Periodicals, Inc. Jrl Fut Mark 22:959–981, 2002     

The valuation of European options when asset returns are autocorrelated

This article derives the closed‐form formula for a European option on an asset with returns following a continuous‐time type of first‐order moving average process, which is called an MA(1)‐type option. The pricing formula of these options is similar to that of Black and Scholes, except for the total volatility input. Specifically, the total volatility input of MA(1)‐type options is the conditional standard deviation of continuous‐compounded returns over the option's remaining life, whereas the total volatility input of Black and Scholes is indeed the diffusion coefficient of a geometric Brownian motion times the square root of an option's time to maturity. Based on the result of numerical analyses, the impact of autocorrelation induced by the MA(1)‐type process is significant to option values even when the autocorrelation between asset returns is weak. © 2006 Wiley Periodicals, Inc. Jrl Fut Mark 26:85–102, 2006     

中国开放式基金收益及其波动性的周内效应研究

了解基金收益及其波动性是否存在周内效应对投资者非常重要,投资者可以利用收益及其波动性的变动信息调整投资组合,增加投资收益。运用均值方程含有虚拟变量的GARCH(1,1)模型和条件方差方程含有虚拟变量的修正的GARCH(1,1)模型,我们分别对2003年6月1日至2005年8月18日期间中国开放式基金收益的周内效应和收益波动性的周内效应进行实证研究,结果显示,在研究期间内样本基金收益及收益的波动性在周三这一天显著不同于其他交易日,即存在“周三效应”。     

Forecasting volatility

The forecasting ability of the most popular volatility forecasting models is examined and an alternative model developed. Existing models are compared in terms of four attributes: (1) the relative weighting of recent versus older observations, (2) the estimation criterion, (3) the trade‐off in terms of out‐of‐sample forecasting error between simple and complex models, and (4) the emphasis placed on large shocks. As in previous studies, we find that financial markets have longer memories than reflected in GARCH(1,1) model estimates, but find this has little impact on outofsample forecasting ability. While more complex models which allow a more flexible weighting pattern than the exponential model forecast better on an in‐sample basis, due to the additional estimation error introduced by additional parameters, they forecast poorly out‐of‐sample. With the exception of GARCH models, we find that models based on absolute return deviations generally forecast volatility better than otherwise equivalent models based on squared return deviations. Among the most popular time series models, we find that GARCH(1,1) generally yields better forecasts than the historical standard deviation and exponentially weighted moving average models, though between GARCH and EGARCH there is no clear favorite. However, in terms of forecast accuracy, all are dominated by a new, simple, nonlinear least squares model, based on historical absolute return deviations, that we develop and test here. © 2005 Wiley Periodicals, Inc. Jrl Fut Mark 25:465–490, 2005     

The Effect of Sport Sponsorship Programs of Various Sport Events on Stock Price Behavior During a Sport Event

This paper examines sporting event's spillover effect to investor's behavior through event study analysis using the GARCH (p,q) model, focusing on the stock price effects of a sport sponsorship program during and after a sporting event. Studying stock price behavior during a sporting event is attempted for the first time in the marketing and sponsorship literature. First, we provide some summary points from the review of 40 research works and interpretive claims, based on a conceptual and theoretical framework. Second, we consider daily stock returns of 28 listed companies that have sponsored 15 major sports events during the period 2000–2009, in order to examine the effect of major sporting events on sponsors’ stock returns and volatility. The three research hypotheses are supported. Research results show that stock returns and volatility changed significantly during and after the sporting event compared to pre-event period. Results show that stock price effects caused by sports events’ sponsorship programs are firm-specific, as well as sporting event-specific. The findings of this study are of high value for promotion managers as it allows them to become more critically aware of the practical wisdom of sporting events.     

Emerging Equity Market Volatility

Abstract

This paper considers two emerging markets that are under-researched, Kenya and Nigeria. It offers a comprehensive view of four time properties that emerged from the empirical time series literature on asset returns: (1) the predictability of returns from past observations; (2) the auto-regressive behavior of conditional volatility; (3) the asymmetric response of conditional volatility to innovations; and (4) the conditional variance risk premium. Results of the exponential GARCH (EGARCH) model indicate that asymmetric volatility found in the U.S. and other developed markets also characterized the Nigerian stock exchange. In Kenya, however, the asymmetric volatility coefficient is significant and positive, suggesting that positive shocks increase volatility more than negative shocks of an equal magnitude. The Nairobi Stock Exchange (KSE) returns series report negative but insignificant risk-premium parameters. In Nigeria (NSE), return series exhibit a significant and positive time-varying risk premium. The results also show that expected returns are predictable, that the auto-regressive return parameters (? ₁ ) are significant in both Kenya and Nigeria. Finally, the GARCH parameter (b) is statistically significant, indicating that volatility persistence is present in the two emerging markets studied.     

Pricing FTSE 100 index options under stochastic volatility

The autoregressive conditional heteroscedasticity/generalized autoregressive conditional heteroscedasticity (ARCH/GARCH) literature and studies of implied volatility clearly show that volatility changes over time. This article investigates the improvement in the pricing of Financial Times‐Stock Exchange (FTSE) 100 index options when stochastic volatility is taken into account. The major tool for this analysis is Heston’s (1993) stochastic volatility option pricing formula, which allows for systematic volatility risk and arbitrary correlation between underlying returns and volatility. The results reveal significant evidence of stochastic volatility implicit in option prices, suggesting that this phenomenon is essential to improving the performance of the Black–Scholes model (Black & Scholes, 1973) for FTSE 100 index options. © 2001 John Wiley & Sons, Inc. Jrl Fut Mark 21:197–211, 2001     

Predicting financial volatility: High‐frequency time‐series forecasts vis‐à‐vis implied volatility

Recent evidence suggests option implied volatilities provide better forecasts of financial volatility than time‐series models based on historical daily returns. In this study both the measurement and the forecasting of financial volatility is improved using high‐frequency data and long memory modeling, the latest proposed method to model volatility. This is the first study to extract results for three separate asset classes, equity, foreign exchange, and commodities. The results for the S&P 500, YEN/USD, and Light, Sweet Crude Oil provide a robust indication that volatility forecasts based on historical intraday returns do provide good volatility forecasts that can compete with and even outperform implied volatility. © 2004 Wiley Periodicals, Inc. Jrl Fut Mark 24:1005–1028, 2004     

Options listings and individual equity volatility

This article examines the effect of options introduction on the conditional volatility of 1,576 individual firms over the 1973–1996 time period. With the use of a GJR‐GARCH specification for daily volatility, it is found, for the majority of firms, that option listing does not impact the underlying equity security. Listing effects are identified for a small subset of firms, specifically smaller firms with high trading volume and/or volatility. For these firms there is evidence of a change in the conditional volatility process after option listing, and it is concluded that options continue to provide additional information about the underlying equity for these companies. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27: 1–27, 2007     

Value at risk and conditional extreme value theory via markov regime switching models

This study develops a new conditional extreme value theory‐based (EVT) model that incorporates the Markov regime switching process to forecast extreme risks in the stock markets. The study combines the Markov switching ARCH (SWARCH) model (which uses different sets of parameters for various states to cope with the structural changes for measuring the time‐varying volatility of the return distribution) with the EVT to model the tail distribution of the SWARCH processed residuals. The model is compared with unconditional EVT and conditional EVT‐GARCH models to estimate the extreme losses in three leading stock indices: S&P 500 Index, Hang Seng Index and Hang Seng China Enterprise Index. The study found that the EVT‐SWARCH model outperformed both the GARCH and SWARCH models in capturing the non‐normality and in providing accurate value‐at‐risk forecasts in the in‐sample and out‐sample tests. The EVTSWARCH model, which exhibits the features of measuring the volatility of a heteroscedastic financial return series and coping with the non‐normality owing to structural changes, can be an alternative measure of the tail risk. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:155–181, 2008     

The information content of implied volatility in agricultural commodity markets

In this article we compare the incremental information content of lagged implied volatility to GARCH models of conditional volatility for a collection of agricultural commodities traded on the New York Board of Trade. We also assess the relevance of the additional information provided by the implied volatility in a risk management framework. It is first shown that past squared returns only marginally improve the information content provided by the lagged implied volatility. Secondly, value‐at‐risk (VaR) models that rely exclusively on lagged implied volatility perform as well as VaR models where the conditional variance is modelled according to GARCH type processes. These results indicate that the implied volatility for options on futures contracts in agricultural commodity markets provides relevant volatility information that can be used as an input to VaR models. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23:441–454, 2003     

The Information Content of Model‐Free Implied Volatility

This study examines the information content of model‐free implied volatility (MFIV) estimates with respect to the options and futures markets in Hong Kong. In this study, the volatility forecasting performance of MFIV is compared, using different prediction horizons, to IV estimates based on Black's futures option pricing model (BIV) and time‐series forecasts based on historical volatility (TS‐HV). The results show that the BIV prediction is unbiased for different horizon forecasts. MFIV outperforms TS‐HV forecasts and, most importantly, BIV subsumes the information content of both MFIV and TS‐HV forecasts. The results are largely maintained for next‐day forecasts but the forecasting quality of the two IV measures declines as expiration day approaches. The information contents of MFIV and TS‐HV forecasts are complementary. © 2012 Wiley Periodicals, Inc. Jrl Fut Mark 32:792‐806, 2012     

The specification of GARCH models with stochastic covariates

A number of studies investigate whether various stochastic variables explain changes in return volatility by specifying the variables as covariates in a GARCH(1, 1) or EGARCH(1, 1) model. The authors show that these models impose an implicit constraint that can obscure the true role of the covariates in the analysis. They illustrate the problem by reconsidering the role of contemporaneous trading volume in explaining ARCH effects in daily stock returns. Once the constraint imposed in earlier research is relaxed, it is found that specifying volume as a covariate does little to diminish the importance of lagged squared returns in capturing the dynamics of volatility. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:911–934, 2008     

Realized volatility and correlation in energy futures markets

Using high‐frequency returns, realized volatility and correlation of the NYMEX light, sweet crude oil, and Henry‐Hub natural gas futures contracts are examined. The unconditional distributions of daily returns and daily realized variances are non‐Gaussian, whereas the distributions of the standardized returns (normalized by the realized standard deviation) and the (logarithms of) realized standard deviations appear approximately Gaussian. The (logarithms of) standard deviations exhibit long‐memory, but the realized correlation between the two futures does not, implying rather weak inter‐market linkage in the long run. There is evidence of asymmetric volatility for natural gas but not for crude oil futures. Finally, realized crude oil futures volatility responds with an increase in the weeks immediately before the OPEC events recommending price increases. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:993–1011, 2008     

Time‐varying jump risk premia in stock index futures returns

This study tests the presence of time‐varying risk premia associated with extreme news events or jumps in stock index futures return. The model allows for a dynamic jump component with autoregressive jump intensity, long‐range dependence in volatility dynamics, and a volatility in mean structure separately for the normal and extreme news events. The results show significant jump risk premia in four stock market index futures returns including the DAX, FTSE, Nikkei, and S&P500 indices. Our results are robust to various specifications of conditional variance including the plain GARCH, component GARCH, and Fractionally Integrated GARCH models. We also find the time‐varying risk premium associated with normal news events is not significant across all indices. © 2011 Wiley Periodicals, Inc. Jrl Fut Mark 32:639–659, 2012