Multivariate Modeling of Daily REIT Volatility

This paper examines volatility in REITs using a multivariate GARCH based model. The Multivariate VAR–GARCH technique documents the return and volatility linkages between REIT sub-sectors and also examines the influence of other US equity series. The motivation is for investors to incorporate time-varyng volatility and correlations in their portfolio selection. The results illustrate the differences in results when higher frequency daily data is tested in comparison to the monthly data that has been commonly used in the existing literature. The linkages both within the REIT sector and between REITs and related sectors such as value stocks are weaker than commonly found in monthly studies. The broad market would appear to be more influential in the daily case.     

Evaluating portfolio Value-at-Risk using semi-parametric GARCH models

In this paper we examine the usefulness of multivariate semi-parametric GARCH models for evaluating the Value-at-Risk (VaR) of a portfolio with arbitrary weights. We specify and estimate several alternative multivariate GARCH models for daily returns on the S&P 500 and Nasdaq indexes. Examining the within-sample VaRs of a set of given portfolios shows that the semi-parametric model performs uniformly well, while parametric models in several cases have unacceptable failure rates. Interestingly, distributional assumptions appear to have a much larger impact on the performance of the VaR estimates than the particular parametric specification chosen for the GARCH equations.     

Options on realized variance by transform methods: a non-affine stochastic volatility model

In this paper we study the pricing and hedging of options on realized variance in the 3/2 non-affine stochastic volatility model by developing efficient transform-based pricing methods. This non-affine model gives prices of options on realized variance that allow upward-sloping implied volatility of variance smiles. Heston's model [Rev. Financial Stud., 1993, 6, 327–343], the benchmark affine stochastic volatility model, leads to downward-sloping volatility of variance smiles—in disagreement with variance markets in practice. Using control variates, we propose a robust method to express the Laplace transform of the variance call function in terms of the Laplace transform of the realized variance. The proposed method works in any model where the Laplace transform of realized variance is available in closed form. Additionally, we apply a new numerical Laplace inversion algorithm that gives fast and accurate prices for options on realized variance, simultaneously at a sequence of variance strikes. The method is also used to derive hedge ratios for options on variance with respect to variance swaps.     

Volatility forecasts and at-the-money implied volatility: a multi-component ARCH approach and its relation to market models

This article explores the relationships between several forecasts for the volatility built from multi-scale linear ARCH processes, and linear market models for the forward variance. This shows that the structures of the forecast equations are identical, but with different dependencies on the forecast horizon. The process equations for the forward variance are induced by the process equations for an ARCH model, but postulated in a market model. In the ARCH case, they are different from the usual diffusive type. The conceptual differences between both approaches and their implication for volatility forecasts are analysed. The volatility forecast is compared with the realized volatility (the volatility that will occur between date t and t + ΔT), and the implied volatility (corresponding to an at-the-money option with expiry at t + ΔT). For the ARCH forecasts, the parameters are set a priori. An empirical analysis across multiple time horizons ΔT shows that a forecast provided by an I-GARCH(1) process (one time scale) does not capture correctly the dynamics of the realized volatility. An I-GARCH(2) process (two time scales, similar to GARCH(1,1)) is better, while a long-memory LM-ARCH process (multiple time scales) replicates correctly the dynamics of the implied and realized volatilities and delivers consistently good forecasts for the realized volatility.     

波动率风险及风险价格——来自中国A股市场的证据

本文应用Fama-Macbeth估计方法,以1997年2月至2009年6月中国A股股票为样本,考察股票市场波动率风险及其风险价格的特征。研究表明:波动率风险是一个显著的横截面定价因子,其风险价格为负,该结论不受流动性及市场偏度因子、待检资产改变、波动率模型设定的影响;在资产定价模型中引入波动率风险因子有利于解释规模效应和账面市值比效应异象。波动率的风险因子可以涵盖部分宏观经济变量的定价信息,规模因子是波动率风险因子的代理变量。     

A multivariate Lévy process model with linear correlation

In this paper, we develop a multivariate risk-neutral Lévy process model and discuss its applicability in the context of the volatility smile of multiple assets. Our formulation is based upon a linear combination of independent univariate Lévy processes and can easily be calibrated to a set of one-dimensional marginal distributions and a given linear correlation matrix. We derive conditions for our formulation and the associated calibration procedure to be well-defined and provide some examples associated with particular Lévy processes permitting a closed-form characteristic function. Numerical results of the option premiums on three currencies are presented to illustrate the effectiveness of our formulation with different linear correlation structures.     

Empirical analysis of dynamic correlations of stock returns: evidence from Chinese A-share and B-share markets

This paper examines the dynamic correlation structure between A-share and B-share stock returns based on three different measures of correlation coefficients. Testing the models by employing daily stock-return data for the period from 1996 through 2003, we reach the following empirical conclusions. First, the correlation coefficients between A-share and B-share stock returns are time varying. Second, the dynamic path of the correlation coefficients indicates that the correlation coefficients are significantly correlated with the trend factor. Third, there is a substantial spillover effect from the Asian crisis to Chinese stock-return dynamic correlations. Fourth, the evidence suggests that the time-varying correlations are significantly associated with excessive trading activity as measured by excessive trading volumes and high–low price differentials. Fifth, the correlation between A-share and B-share markets has increased since the relaxation of the restriction on B-share market investments by domestic investors.     

Capital Asset Pricing Model and Stochastic Volatility: A Case Study of India

The existing literature demonstrates that under a general equilibrium model, the performance of the Capital Asset Pricing Model (CAPM) can be improved significantly by using conditional consumption and market return volatilities as factors. This article tests the validity of these factors explaining stock return differences using a less developed country (India) as a case study. While the earlier studies used panel data to test CAPM, we use portfolios sorted by size and book-to-market equity (BE/ME) ratio. We found that conditional volatility has a limited effect on firms with large capitalization but a significant impact on small-growth and small-value firms.     

Pricing equity options everywhere

Finite difference methods are a popular technique for pricing American options. Since their introduction to finance by Brennan and Schwartz their use has spread from vanilla calls and puts on one stock to path-dependent and exotic options on multiple assets. Despite the breadth of the problems they have been applied to, and the increased sophistication of some of the newer techniques, most approaches to pricing equity options have not adequately addressed the issues of unbounded computational domains and divergent diffusion coefficients. In this article it is shown that these two problems are related and can be overcome using multiple grids. This new technique allows options to be priced for all values of the underlying, and is illustrated using standard put options and the call on the maximum of two stocks. For the latter contract, I also derive a characterization of the asymptotic continuation region in terms of a one-dimensional option pricing problem, and give analytic formulae for the perpetual case.     

An event study of price movements following realized jumps

Price jumps are mostly related to investor reactions to unexpected extreme news. We perform an event study of price movements after jumps to analyse if investors’ reactions are affected by psychological biases. We employ recent non-parametric methods based on intraday returns to separate large price movements that are related to unexpected news from those merely caused by periods of high volatility. In general, we find evidence for irrational pricing, which can be associated with investors’ optimistic behavior in a bull market and the pessimism prevailing in a bear market. Furthermore, our analysis confirms the conjecture that small firms are more subject to speculative trading than large firms.     

No-dynamic-arbitrage and market impact

Starting from a no-dynamic-arbitrage principle that imposes that trading costs should be non-negative on average and a simple model for the evolution of market prices, we demonstrate a relationship between the shape of the market impact function describing the average response of the market price to traded quantity and the function that describes the decay of market impact. In particular, we show that the widely assumed exponential decay of market impact is compatible only with linear market impact. We derive various inequalities relating the typical shape of the observed market impact function to the decay of market impact, noting that, empirically, these inequalities are typically close to being equalities.     

Common Volatility: An Empirical Investigation of Closed-End Country Funds

The study of international integration of equity markets has received a great deal of interest. This paper investigates whether returns of forty-one closed-end country funds share a common volatility process with three comparable return series: the underlying net asset value (NAV), U.S. stock market returns, and foreign stock market returns. Country funds are a natural setting to test for international market integration, as they are traded in the U.S. market, whereas their underlying assets are traded in foreign stock markets. Our results indicate that only a few emerging markets' country funds share common volatility processes with their comparable asset returns. This, in turn, suggests weak linkages through the second moment of related assets.     

International stock markets interactions and conditional correlations

This paper investigates the transmission of price and volatility spillovers across the US and European stock markets in bivariate combinations. The framework used encompasses the most popular multivariate GARCH models, with News Impact Surfaces employed for interpretation. By using synchronous data the dynamic conditional correlation model (Engle, R., 2002. Dynamic conditional correlation: a simple class of multivariate GARCH models. Journal of Business and Economic Statistics 20, 339–350) is found to best capture the relationships for over half of the bivariate combinations of markets. Other findings include volatility spillovers from the US to European markets, and a reverse spillover. In addition, the magnitude of the correlation between markets is higher not only for negative shocks in both markets, but also when a combination of shocks of opposite signs occurs.     

A new closed-form solution as an extension of the Black–Scholes formula allowing smile curve plotting

In this paper, as a generalization of the Black–Scholes (BS) model, we elaborate a new closed-form solution for a uni-dimensional European option pricing model called the J-model. This closed-form solution is based on a new stochastic process, called the J-process, which is an extension of the Wiener process satisfying the martingale property. The J-process is based on a new statistical law called the J-law, which is an extension of the normal law. The J-law relies on four parameters in its general form. It has interesting asymmetry and tail properties, allowing it to fit the reality of financial markets with good accuracy, which is not the case for the normal law. Despite the use of one state variable, we find results similar to those of Heston dealing with the bi-dimensional stochastic volatility problem for pricing European calls. Inverting the BS formula, we plot the smile curve related to this closed-form solution. The J-model can also serve to determine the implied volatility by inverting the J-formula and can be used to price other kinds of options such as American options.     

Volatility and market structure

This study examines volatility within three related intra-day series – transaction returns, quote midpoint returns, and limit order book midpoint returns – for a set of NYSE-listed stocks. We document statistically significant GARCH effects both overall and surrounding earnings announcements in all three series for the majority of stocks in the sample. We then compare the extent of volatility clustering among the series. In addition, the relation between volatility and market structure is examined via a set of cross-sectional regressions, and relations among the series over time are studied in a vector autoregressive framework.     

Conditional Volatility of Equity Real Estate Investment Trust Returns: A Pre- and Post-1993 Comparison

We examine the dynamic behavior of Equity Real Estate Investment Trust (EREIT) volatility in a GARCH context 1972–2006 using monthly EREIT returns, and comparing volatility performance for “early” Equity REITs 1972–1992 with that of “modern” EREITs 1993–2006. Consistent with findings for conventional firms, we find that EREIT conditional volatility is time-varying, persistent, and predictable. There is a positive relationship between expected return and expected risk in EREIT stocks pre-1993, but the relationship disappears after 1993. We find no evidence that negative shocks affect EREIT volatility differently from positive ones in either time period. Different from reported results for conventional firms, we find that changes in the conditional volatility of fundamental macroeconomic variables have strong explanatory value for future changes in EREIT volatility. Finally, comparing EREIT volatility performance with volatility in the Russell 2000 Index, a proxy for small stocks, we find that EREIT volatility behaves differently from that of small stocks in many respects, indicating that risks in the small stock index cannot effectively proxy for risks in the EREIT market.

Volatility Transmission in the Real Estate Spot and Forward Markets

How shocks in one market influence the returns and volatility of other markets has been an important question for portfolio managers. In the finance literature, many studies found evidence of volatility spillovers across international markets, as well as between spot and futures markets. Although real estate is often regarded as a good vehicle for diversification, the dynamics of its volatility transmission have been largely ignored. This paper provides the first study to examine volatility spillovers between the spot and forward (pre-sale) index returns of the Hong Kong real estate market through a bivariate GARCH model. Transaction-based indices were used so that our volatility modelling was free from any smoothing problem. Our results showed that real estate returns exhibited volatility clustering, and the volatility of the forward market was more sensitive to shocks than the spot market. Moreover, volatility was mainly transmitted from the forward market to the spot market, but not vice versa.

Forecasting volatility in GARCH models with additive outliers

We model the volatility of a single risky asset using a multifactor (matrix) Wishart affine process, recently introduced in finance by Gourieroux and Sufana. As in standard Duffie and Kan affine models the pricing problem can be solved through the Fast Fourier Transform of Carr and Madan. A numerical illustration shows that this specification provides a separate fit of the long-term and short-term implied volatility surface and, differently from previous diffusive stochastic volatility models, it is possible to identify a specific factor accounting for the stochastic leverage effect, a well-known stylized fact of the FX option markets analysed by Carr and Wu.     

Forecasting Commodity Market Returns Volatility: A Hybrid Ensemble Learning GARCH-LSTM based Approach

This study investigates the advantage of combining the forecasting abilities of multiple generalized autoregressive conditional heteroscedasticity (GARCH)-type models, such as the standard GARCH (GARCH), exponential GARCH (eGARCH), and threshold GARCH (tGARCH) models with advanced deep learning methods to predict the volatility of five important metals (nickel, copper, tin, lead, and gold) in the Indian commodity market. This paper proposes integrating the forecasts of one to three GARCH-type models into an ensemble learning-based hybrid long short-term memory (LSTM) model to forecast commodity price volatility. We further evaluate the forecasting performance of these models for standalone LSTM and GARCH-type models using the root mean squared error, mean absolute error, and mean fundamental percentage error. The results highlight that combining the information from the forecasts of multiple GARCH types into a hybrid LSTM model leads to superior volatility forecasting capability. The SET-LSTM, which represents the model that combines forecasts of the GARCH, eGARCH, and tGARCH into the LSTM hybrid, has shown the best overall results for all metals, barring a few exceptions. Moreover, the equivalence of forecasting accuracy is tested using the Diebold–Mariano and Wilcoxon signed-rank tests.     

Imperfect Information and Stock Market Volatility

The purpose of this paper is to (1) develop a model to show how imperfect information can create excess volatility in asset returns and (2) provide empirical evidence consistent with the model. In this framework, variations in information quality cause the market prices to fluctuate more than the corresponding economic fundamentals. Using high‐frequency data from 1988 to 2002, the empirical evidence supports the predictions of the model by showing that economic volatility, defined as squared deviations of the quarterly gross domestic product (GDP) growth rate from its long‐run trend, can explain about half of the variation in S&P 500‐stock index quarterly volatility.