Liability driven investment with alternative assets: Evidence from Brazil

We study the portfolio choice problem for an asset-liability investor who invests in stocks, equity mutual funds, government bonds, short term interest, hedge funds, listed real estate, and commodities futures available in Brazil. Inflation and real interest play as important risk sources. We estimate the asset classes and liabilities time-varying conditional covariance structure using an asymmetric multivariate dynamic conditional correlation GARCH model and compare the asset-liability portfolio's global minimum variance allocation with Brazilian pension funds' market portfolio. The conditional covariance structure provides insights about the complex dynamic relationships between the asset classes and liabilities. We find that some (though not all) Brazilian alternative assets render strong diversification and liabilities hedging benefits for asset-liability investors. There are significant strategic asset allocation differences between the market portfolio and the liability driven portfolio as given by our model. We, therefore, question the Brazilian pension funds' allocation.     

Stock index futures trading and volatility in international equity markets

This article examines stock market volatility before and after the introduction of equity‐index futures trading in twenty‐five countries, using various models that account for asynchronous data, conditional heteroskedasticity, asymmetric volatility responses, and the joint dynamics of each country's index with the world‐market portfolio. We found that futures trading is related to an increase in conditional volatility in the United States and Japan, but in nearly every other country, we found either no significant effect or a volatility‐dampening effect. This result appears to be robust to model specification and is corroborated by further analysis of the relationship between volatility, trading volume, and open interest in stock futures. An increase in conditional covariance between country‐specific and world returns at the time of futures listing is also documented. © 2000 John Wiley & Sons, Inc. Jrl Fut Mark 20:661–685, 2000     

中国证券市场波动的区制关联性

应用单变量和二元向量SW-ARCH模型,本文发现我国证券市场收益率波动具有明显的"区制转移"特征,可以将其分为"高波动"和"低波动"两个区制.在"高波动区制"下,沪深两市间具有明显的波动"溢出"和"传染"特征,市场整体风险强;相反,在"低波动区制"下,市场间主要表现"低系统风险"特征,负相关的波动关联性使证券市场具有较强的风险分散功能和较高的资金配置效率.     

Fractional cointegration and futures hedging

This article examines the performance of various hedge ratios estimated from different econometric models: The FIEC model is introduced as a new model for estimating the hedge ratio. Utilized in this study are NSA futures data, along with the ARFIMA-GARCH approach, the EC model, and the VAR model. Our analysis identifies the prevalence of a fractional cointegration relationship. The effects of incorporating such a relationship into futures hedging are investigated, as is the relative performance of various models with respect to different hedge horizons. Findings include: (i) Incorporation of conditional heteroskedasticity improves hedging performance; (ii) the hedge ratio of the EC model is consistently larger than that of the FIEC model, with the EC providing better post-sample hedging performance in the return–risk context; (iii) the EC hedging strategy (for longer hedge horizons of ten days or more) incorporating conditional heteroskedasticty is the dominant strategy; (iv) incorporating the fractional cointegration relationship does not improve the hedging performance over the EC model; (v) the conventional regression method provides the worst hedging outcomes for hedge horizons of five days or more. Whether these results (based on the NSA index) can be generalized to other cases is proposed as a topic for further research. © 1999 John Wiley & Sons, Inc. Jrl Fut Mark 19: 457–474, 1999     

Semistatic hedging and pricing American floating strike lookback options

We price an American floating strike lookback option under the Black–Scholes model with a hypothetic static hedging portfolio (HSHP) composed of nontradable European options. Our approach is more efficient than the tree methods because recalculating the option prices is much quicker. Applying put–call duality to an HSHP yields a tradable semistatic hedging portfolio (SSHP). Numerical results indicate that an SSHP has better hedging performance than a delta-hedged portfolio. Finally, we investigate the model risk for SSHP under a stochastic volatility assumption and find that the model risk is related to the correlation between asset price and volatility.     

Estimation and hedging effectiveness of time‐varying hedge ratio: Flexible bivariate garch approaches

Bollerslev's ( 1990 , Review of Economics and Statistics, 52, 5–59) constant conditional correlation and Engle's (2002, Journal of Business & Economic Statistics, 20, 339–350) dynamic conditional correlation (DCC) bivariate generalized autoregressive conditional heteroskedasticity (BGARCH) models are usually used to estimate time‐varying hedge ratios. In this study, we extend the above model to more flexible ones to analyze the behavior of the optimal conditional hedge ratio based on two (BGARCH) models: (i) adopting more flexible bivariate density functions such as a bivariate skewed‐t density function; (ii) considering asymmetric individual conditional variance equations; and (iii) incorporating asymmetry in the conditional correlation equation for the DCC‐based model. Hedging performance in terms of variance reduction and also value at risk and expected shortfall of the hedged portfolio are also conducted. Using daily data of the spot and futures returns of corn and soybeans we find asymmetric and flexible density specifications help increase the goodness‐of‐fit of the estimated models, but do not guarantee higher hedging performance. We also find that there is an inverse relationship between the variance of hedge ratios and hedging effectiveness. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 30:71–99, 2010     

Volatility spillover and hedging effectiveness among China and emerging Asian Islamic equity indexes

We study the volatility spillover between China and Asian Islamic stock markets. We use a sample of six Islamic MSCI indices from the Asian region, namely China, India, Malaysia, Indonesia, Korea and Thailand obtained from MSCI (Morgan Stanley Capital International). In this paper we analyze the importance of considering spillover effects between emerging Asian Islamic indexes based on the Bivariate VARMA-BEKK-AGARCH model of McAleer et al. (2009), which includes spillover and asymmetric effects. We compute after the effectiveness of portfolio diversification based on the conditional volatility of returns series. Results show a significant positive and negative return spillover from China to selected Asian Islamic stock market and bidirectional volatility spillovers between China, Korea and Thailand Islamic market showing evidence of short-term predictability on Islamic Chinese stock market movements. However there is no short term volatility persistence in India, Indonesia and Malaysia. GARCH results show no persistence in volatility spillover effect in long term from Chinese to Indian, Indonesian and Korean Islamic stock market. Our findings are beneficial for international portfolio diversification for policy makers and investors since the results of portfolio management and hedging effectiveness ratio are different to previous studies.     

An empirical comparison of continuous time models of the short term interest rate

This article tests the performance of a wide variety of well-known continuous time models—with particular emphasis on the Black, Derman, and Toy (1990; henceforth BDT) term structure model—in capturing the stochastic behavior of the short term interest rate volatility. Many popular interest rate models are nested within a more flexible time-varying BDT framework that allows us to compare the models and find the proper specification of the dynamics of short rates. The empirical results indicate that the equilibrium models that do not allow the drift and diffusion parameters to vary over time and parameterize the volatility only as a function of interest rate levels overemphasize the sensitivity of volatility to the level of interest rate and fail to model adequately the serial correlation in conditional variances. On the other hand, the GARCH-based arbitrage-free models with time-dependent parameters in the drift and diffusion functions define the volatility only as a function of unexpected information shocks and fail to capture adequately the relationship between interest rate levels and volatility. This study shows that the most successful models in capturing the dynamics of short term interest rates are those that introduce time-dependent parameters to the short rate process and define the conditional volatility as a function of both the interest rate levels and the last period's unexpected news. © 1999 John Wiley & Sons, Inc. Jrl Fut Mark 19: 777–797, 1999     

Quantiles of the Euler Scheme for Diffusion Processes and Financial Applications

In this paper we briefly present the results obtained in our paper ( Talay and Zheng 2002a ) on the convergence rate of the approximation of quantiles of the law of one component of  ( X_t )  , where  ( X_t )  is a diffusion process, when one uses a Monte Carlo method combined with the Euler discretization scheme. We consider the case where  ( X_t )  is uniformly hypoelliptic (in the sense of Condition (UH) below), or the inverse of the Malliavin covariance of the component under consideration satisfies the condition (M) below. We then show that Condition (M) seems widely satisfied in applied contexts. We particularly study financial applications: the computation of quantiles of models with stochastic volatility, the computation of the VaR of a portfolio, and the computation of a model risk measurement for the profit and loss of a misspecified hedging strategy.     

Volatility and shock interactions and risk management implications: Evidence from the U.S. and frontier markets

The study affords comprehensive evidence of shock and volatility interactions between stock markets of each of the twenty four frontier markets and the U.S. for the period 2006:01 to 2015:07. The results from the recent EDCC-GARCH model of Nakatani and Teräsvirta (2009), which permits for concurrent estimation of shock and volatility interactions as well as dynamic conditional correlations (DCC) across assets, shows unidirectional shock and volatility transmissions from the U.S. to the frontier markets. The conditional correlation between the U.S. and each frontier market is very low or negative, offering diversification benefits to U.S. investors. The DCC exhibits slow decay and is insignificantly impacted by previous period's shocks. The results are very intuitive for optimal portfolio allocations using the traditional capital-based as well as the risk-based allocations. The risk parity approach to portfolio management increases (reduces) allocations to lower (higher) risk assets to improve portfolio diversification while increasing the risk-adjusted returns.     

Three Simple Techniques to Analyze a Complex Economic Phenomenon: The Case of Profits

This paper seeks to characterize the behavior of profits over the business cycle as a model for analyzing any economic series by a practicing business economist. It addresses three fundamental questions about profits that are common and critical to identifying the behavior of any macroeconomic series—mean-reversion, volatility, and trend. First, does profit growth over time exhibit mean-reverting behavior? Second, how volatile are profits, and does this volatility obscure the message of average profit growth? Third, how can we estimate a long-run trend growth component for profits and thereby separate profit cycles from its long-run trend growth component?     

Assessing the asymmetric volatility linkages of energy and agricultural commodity futures during low and high volatility regimes

This study investigated the volatility linkages between energy and agricultural futures, including possible causes for these comovements, such as external macroeconomic and financial shocks during low and high volatility regimes. A combination of Markov-switching regressions and quadrivariate VAR–DCC–GARCH and VAR–BEKK–GARCH modeling revealed that external shocks have an asymmetric effect on the relationship of these assets with higher cross-correlations reported during high volatility regimes. This comovement effect outweighs the substitution effect between energy and agricultural products. Furthermore, the quadrivariate VAR–BEKK–GARCH model provides strong evidence of a bidirectional price volatility spillover between the agricultural and energy markets during periods of high volatility. Overall, the results suggest that energy futures can be effectively used for hedging in a portfolio comprising agricultural futures (and vice versa), while a combination of macroeconomic and financial index futures can serve as an effective hedging tool in investment portfolios comprising both energy and agricultural commodities.     

The Introduction of Derivatives on the Dow Jones Industrial Average and Their Impact on the Volatility of Component Stocks

This article examines the impact of trading in the Dow Jones Industrial Average (DJIA) index futures and futures options on the conditional volatility of component stocks. It investigates the contention that the introduction of futures and futures options on the DJIA could increase volatility in the 30 stocks comprising the DJIA. The conditional volatility of intraday returns for each stock before and after the introduction of derivatives is estimated with the Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model. Estimated parameters of conditional volatility in prefutures and postfutures periods are then compared to determine if the estimated parameters have changed significantly after the introduction of the various derivatives. The results suggest that the introduction of index futures and futures options on the DJIA has produced no structural changes in the conditional volatility of component stocks. © 2001 John Wiley & Sons, Inc. Jrl Fut Mark 21: 633–653, 2001     

Hedging and value at risk

In this article, it is shown that although minimum‐variance hedging unambiguously reduces the standard deviation of portfolio returns, it can increase both left skewness and kurtosis; consequently the effectiveness of hedging in terms of value at risk (VaR) and conditional value at risk (CVaR) is uncertain. The reduction in daily standard deviation is compared with the reduction in 1‐day 99% VaR and CVaR for 20 cross‐hedged currency portfolios with the use of historical simulation. On average, minimum‐variance hedging reduces both VaR and CVaR by about 80% of the reduction in standard deviation. Also investigated, as an alternative to minimum‐variance hedging, are minimum‐VaR and minimum‐CVaR hedging strategies that minimize the historical‐simulation VaR and CVaR of the hedge portfolio, respectively. The in‐sample results suggest that in terms of VaR and CVaR reduction, minimum‐VaR and minimum‐CVaR hedging can potentially yield small but consistent improvements over minimum‐variance hedging. The out‐of‐sample results are more mixed, although there is a small improvement for minimum‐VaR hedging for the majority of the currencies considered. © 2006 Wiley Periodicals, Inc. Jrl Fut Mark 26:369–390, 2006     

ON ARBITRAGE AND DUALITY UNDER MODEL UNCERTAINTY AND PORTFOLIO CONSTRAINTS

We consider the fundamental theorem of asset pricing (FTAP) and the hedging prices of options under nondominated model uncertainty and portfolio constraints in discrete time. We first show that no arbitrage holds if and only if there exists some family of probability measures such that any admissible portfolio value process is a local super‐martingale under these measures. We also get the nondominated optional decomposition with constraints. From this decomposition, we obtain the duality of the super‐hedging prices of European options, as well as the sub‐ and super‐hedging prices of American options. Finally, we get the FTAP and the duality of super‐hedging prices in a market where stocks are traded dynamically and options are traded statically.     

Pricing American options with stochastic volatility: Evidence from S&P 500 futures options

This article is the first attempt to test empirically a numerical solution to price American options under stochastic volatility. The model allows for a mean‐reverting stochastic‐volatility process with non‐zero risk premium for the volatility risk and correlation with the underlying process. A general solution of risk‐neutral probabilities and price movements is derived, which avoids the common negative‐probability problem in numerical‐option pricing with stochastic volatility. The empirical test shows clear evidence supporting the occurrence of stochastic volatility. The stochastic‐volatility model outperforms the constant‐volatility model by producing smaller bias and better goodness of fit in both the in‐sample and out‐of‐sample test. It not only eliminates systematic moneyness bias produced by the constant‐volatility model, but also has better prediction power. In addition, both models perform well in the dynamic intraday hedging test. However, the constant‐volatility model seems to have a slightly better hedging effectiveness. The profitability test shows that the stochastic volatility is able to capture statistically significant profits while the constant volatility model produces losses. © 2000 John Wiley & Sons, Inc. Jrl Fut Mark 20:625–659, 2000     

Volatility and maturity effects in the Nikkei index futures

Many financial data series are found to exhibit stochastic volatility. Some of these time series are constructed from contracts with time-varying maturities. In this paper, we focus on index futures, an important subclass of such time series. We propose a bivariate GARCH model with the maturity effect to describe the joint dynamics of the spot index and the futures-spot basis. The setup makes it possible to examine the Samuelson effect as well as to compare the hedge ratios under scenarios with and without the maturity effect. The Nikkei-225 index and its futures are used in our empirical analysis. Contrary to the Samuelson effect, we find that the volatility of the futures price decreases when the contract is closer to its maturity. We also apply our model to futures hedging, and find that both the optimal hedge ratio and the hedging effectiveness critically depend on both the maturity and GARCH effects. © 1999 John Wiley & Sons, Inc. Jrl Fut Mark 19: 895–909, 1999     

Volatility options: Hedging effectiveness,pricing, and model error

Motivated by the growing literature on volatility options and their imminent introduction in major exchanges, this article addresses two issues. First, the question of whether volatility options are superior to standard options in terms of hedging volatility risk is examined. Second, the comparative pricing and hedging performance of various volatility option pricing models in the presence of model error is investigated. Monte Carlo simulations within a stochastic volatility setup are employed to address these questions. Alternative dynamic hedging schemes are compared, and various option‐pricing models are considered. It is found that volatility options are not better hedging instruments than plain‐vanilla options. Furthermore, the most naïve volatility option‐pricing model can be reliably used for pricing and hedging purposes. © 2006 Wiley Periodicals, Inc. Jrl Fut Mark 26:1–31, 2006     

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     

The Asymmetric Commodity Inventory Effect on the Optimal Hedge Ratio

Hedging strategies for commodity prices largely rely on dynamic models to compute optimal hedge ratios. This study illustrates the importance of considering the commodity inventory effect (effect by which the commodity price volatility increases more after a positive shock than after a negative shock of the same magnitude) in modeling the variance–covariance dynamics. We show by in‐sample and out‐of‐sample forecasts that a commodity price index portfolio optimized by an asymmetric BEKK–GARCH model outperforms the symmetric BEKK, static (OLS), or naïve models. Robustness checks on a set of commodities and by an alternative mean‐variance optimization framework confirm the relevance of taking into account the inventory effect in commodity hedging strategies.