Asset Prices Under Habit Formation and Reference-Dependent Preferences

This article explains the high level and the countercyclical variation of the equity premium in a consumption-based asset pricing model with low large-scale risk aversion. Investors have gain-loss utility over consumption relative to slowly time-varying habit. Stocks deliver low returns in recessions when consumption falls below habit; investors therefore require a high premium for holding stocks. The model's conditional moment restrictions are tested on consumption and asset returns data. The empirical estimate of large-scale risk aversion is low, whereas the estimate of loss aversion agrees with prior experimental evidence.     

Forecasting Equity Premium: Global Historical Average Versus Local Historical Average and Constraints

The equity premium, return on equity minus return on risk-free asset, is expected to be positive. We consider imposing such positivity constraint in local historical average (LHA) in nonparametric kernel regression framework. It is also extended to the semiparametric single index model when multiple predictors are used. We construct the constrained LHA estimator via an indicator function which operates as “model-selection” between the unconstrained LHA and the bound of the constraint (zero for the positivity constraint). We smooth the indicator function by bagging, which operates as “model-averaging” and yields a combined forecast of unconstrained LHA forecasts and the bound of the constraint. The local combining weights are determined by the probability that the constraint is binding. Asymptotic properties of the constrained LHA estimators without and with bagging are established, which show how the positive constraint and bagging can help reduce the asymptotic variance and mean squared errors. Monte Carlo simulations are conducted to show the finite sample behavior of the asymptotic properties. In predicting U.S. equity premium, we show that substantial nonlinearity can be captured by LHA and that the local positivity constraint can improve out-of-sample prediction of the equity premium.     

Asymptotic Inference for Performance Fees and the Predictability of Asset Returns

In this article, we provide analytical, simulation, and empirical evidence on a test of equal economic value from competing predictive models of asset returns. We define economic value using the concept of a performance fee—the amount an investor would be willing to pay to have access to an alternative predictive model used to make investment decisions. We establish that this fee can be asymptotically normal under modest assumptions. Monte Carlo evidence shows that our test can be accurately sized in reasonably large samples. We apply the proposed test to predictions of the U.S. equity premium.     

Estimating the Parameters of Stochastic Volatility Models Using Option Price Data

This article describes a maximum likelihood method for estimating the parameters of the standard square-root stochastic volatility model and a variant of the model that includes jumps in equity prices. The model is fitted to data on the S&P 500 Index and the prices of vanilla options written on the index, for the period 1990 to 2011. The method is able to estimate both the parameters of the physical measure (associated with the index) and the parameters of the risk-neutral measure (associated with the options), including the volatility and jump risk premia. The estimation is implemented using a particle filter whose efficacy is demonstrated under simulation. The computational load of this estimation method, which previously has been prohibitive, is managed by the effective use of parallel computing using graphics processing units (GPUs). The empirical results indicate that the parameters of the models are reliably estimated and consistent with values reported in previous work. In particular, both the volatility risk premium and the jump risk premium are found to be significant.     

The Role of Heterogeneity in Asset Pricing: The Effect of a Clustering Approach

In this article we use a novel clustering approach to study the role of heterogeneity in asset pricing. We present evidence that the equity premium is consistent with a stochastic discount factor (SDF) calculated as the average of the household clusters’ intertemporal marginal rates of substitution in the 1984–2002 period. The result is driven by the skewness of the cluster-based cross-sectional distribution of consumption growth, but cannot be explained by the cross-sectional variance and mean alone. We find that nine clusters are sufficient to explain the equity premium with relative risk aversion coefficient equal to six. The result is robust to various averaging schemes of cluster-based consumption growth used to construct the SDF. Lastly, the analysis reveals that standard approximation schemes of the SDF using individual household data produce unreliable results, implying a negative SDF.     

The Structural Break in the Equity Premium

This article uses Bayesian marginal likelihood analysis to compare univariate models of the stock return behavior and test for structural breaks in the equity premium. The analysis favors a model that relates the equity premium to Markov-switching changes in the level of market volatility and accommodates volatility feedback. For this model, there is evidence of a one-time structural break in the equity premium in the 1940s, with no evidence of additional breaks in the postwar period. The break in the 1940s corresponds to a permanent reduction in the general level of stock market volatility. Meanwhile, there appears to be no change in the underlying risk preferences relating the equity premium to market volatility. The estimated unconditional equity premium drops from an annualized 12% before to the break to 9% after the break.     

Measuring Nonlinear Granger Causality in Mean

We propose model-free measures for Granger causality in mean between random variables. Unlike the existing measures, ours are able to detect and quantify nonlinear causal effects. The new measures are based on nonparametric regressions and defined as logarithmic functions of restricted and unrestricted mean square forecast errors. They are easily and consistently estimated by replacing the unknown mean square forecast errors by their nonparametric kernel estimates. We derive the asymptotic normality of nonparametric estimator of causality measures, which we use to build tests for their statistical significance. We establish the validity of smoothed local bootstrap that one can use in finite sample settings to perform statistical tests. Monte Carlo simulations reveal that the proposed test has good finite sample size and power properties for a variety of data-generating processes and different sample sizes. Finally, the empirical importance of measuring nonlinear causality in mean is also illustrated. We quantify the degree of nonlinear predictability of equity risk premium using variance risk premium. Our empirical results show that the variance risk premium is a very good predictor of risk premium at horizons less than 6 months. We also find that there is a high degree of predictability at the 1-month horizon, that can be attributed to a nonlinear causal effect. Supplementary materials for this article are available online.     

Stock Returns and Expected Business Conditions: Half a Century of Direct Evidence

Using survey data, we characterize directly the impact of expected business conditions on expected excess stock returns. Expected business conditions consistently affect expected excess returns in a counter-cyclical fashion. Moreover, inclusion of expected business conditions in otherwise-standard predictive return regressions substantially reduce the explanatory power of the conventional financial predictors, including the dividend yield, default premium, and term premium, while simultaneously increasing R². Expected business conditions retain predictive power even when including the key nonfinancial predictor, the generalized consumption/wealth ratio. We argue that time-varying expected business conditions likely capture time-varying risk, whereas time-varying consumption/wealth may capture time-varying risk aversion.     

Analysis of a jump-diffusion option pricing model with serially correlated jump sizes

This paper extends the classical jump-diffusion option pricing model to incorporate serially correlated jump sizes which have been documented in recent empirical studies. We model the series of jump sizes by an autoregressive process and provide an analysis on the underlying stock return process. Based on this analysis, the European option price and the hedging parameters under the extended model are derived analytically. Through numerical examples, we investigate how the autocorrelation of jump sizes influences stock returns, option prices and hedging parameters, and demonstrate its effects on hedging portfolios and implied volatility smiles. A calibration example based on real market data is provided to show the advantage of incorporating the autocorrelation of jump sizes.     

A semi-parametric method for estimating the beta coefficients of the hidden two-sided asset return jumps

ABSTRACT

We introduce a new methodology for estimating the parameters of a two-sided jump model, which aims at decomposing the daily stock return evolution into (unobservable) positive and negative jumps as well as Brownian noise. The parameters of interest are the jump beta coefficients which measure the influence of the market jumps on the stock returns, and are latent components. For this purpose, at first we use the Variance Gamma (VG) distribution which is frequently used in modeling financial time series and leads to the revelation of the hidden market jumps' distributions. Then, our method is based on the central moments of the stock returns for estimating the parameters of the model. It is proved that the proposed method provides always a solution in terms of the jump beta coefficients. We thus achieve a semi-parametric fit to the empirical data. The methodology itself serves as a criterion to test the fit of any sets of parameters to the empirical returns. The analysis is applied to NASDAQ and Google returns during the 2006–2008 period.     

Optimal financing and dividend policy with Markovian switching regimes

This work investigates an optimal financing and dividend problem for an insurer whose surplus process is modulated by an observable continuous-time and finite-state Markov chain. We assume that the insurer should never go bankrupt by issuing new equity. The goal of the insurer is to maximize the expected present value of the dividends payout minus the discounted cost of equity issuance. We obtain the optimal policies and explicit expressions for the value functions when the risk reserve process is modeled by both upward jump model and its diffusion approximation. Numerical illustrations of the sensitivities of the model parameters are provided.     

国有企业改革与工资支付结构变革的面板数据分析

本文拟考察在1988-2002年期间国企改革对中国城镇工资支付结构变革的影响、特别是工资决定因素的变化。我们发现对教育的回报在增长,而对工作经验的回报在下降。2002年的数据表明：不断扩大的性别工资差距以及不断增加的非市场因素工资溢价可能均已不再上升。国企改革以及重工业在总体产业结构中比重的不断降低对这些部门职工的工资均已产生影响。我们使用1998-2002年回顾性面板数据提供了关于部门所有制结构、是否是党员以及失业等变量对工资影响的固定效应估计。     

Does sequential augmenting of simple linear heteroscedastic regression reduce variances of ordinary least-squares estimators?

If uncorrelated random variables have a common expected value and decreasing variances, then the variance of a sample mean is decreasing with the number of observations. Unfortunately, this natural and desirable variance reduction property (VRP) by augmenting data is not automatically inherited by ordinary least-squares (OLS) estimators of parameters. We derive a new decomposition for updating the covariance matrices of the OLS which implies conditions for the OLS to have the VRP. In particular, in the case of a straight-line regression, we show that the OLS estimators of intercept and slope have the VRP if the values of the explanatory variable are increasing. This also holds true for alternating two-point experimental designs.     

Pricing power options with a generalized jump diffusion

In this article, the valuation of power option is investigated when the dynamic of the stock price is governed by a generalized jump-diffusion Markov-modulated model. The systematic risk is characterized by the diffusion part, and the non systematic risk is characterized by the pure jump process. The jumps are described by a generalized renewal process with generalized jump amplitude. By introducing NASDAQ Index Model, their risk premium is identified respectively. A risk-neutral measure is identified by employing Esscher transform with two families of parameters, which represent the two parts risk premium. In this article, the non systematic risk premium is considered, based on which the price of power option is studied under the generalized jump-diffusion Markov-modulated model. In the case of a special renewal process with log double exponential jump amplitude, the accurate expressions for the Esscher parameters and the pricing formula are provided. By numerical simulation, the influence of the non systematic risk’s price and the index of the power options on the price of the option is depicted.     

Identifying Bull and Bear Markets in Stock Returns

This article uses a Markov-switching model that incorporates duration dependence to capture nonlinear structure in both the conditional mean and the conditional variance of stock returns. The model sorts returns into a high-return stable state and a low-return volatile state. We label these as bull and bear markets, respectively. The filter identifies all major stock-market downturns in over 160 years of monthly data. Bull markets have a declining hazard functions although the best market gains come at the start of a bull market. Volatility increases with duration in bear markets. Allowing volatility to vary with duration captures volatility clustering.     

A wavelet-based approach to the analysis and modelling of financial time series exhibiting strong long-range dependence: the case of Southeast Europe

This paper demonstrates the utilization of wavelet-based tools for the analysis and prediction of financial time series exhibiting strong long-range dependence (LRD). Commonly emerging markets' stock returns are characterized by LRD. Therefore, we track the LRD evolvement for the return series of six Southeast European stock indices through the application of a wavelet-based semi-parametric method. We further engage the á trous wavelet transform in order to extract deeper knowledge on the returns term structure and utilize it for prediction purposes. In particular, a multiscale autoregressive (MAR) model is fitted and its out-of-sample forecast performance is benchmarked to that of ARMA. Additionally, a data-driven MAR feature selection procedure is outlined. We find that the wavelet-based method captures adequately LRD dynamics both in calm as well as in turmoil periods detecting the presence of transitional changes. At the same time, the MAR model handles with the complicated autocorrelation structure implied by the LRD in a parsimonious way achieving better performance.     

Factor Multivariate Stochastic Volatility via Wishart Processes

This paper proposes a high dimensional factor multivariate stochastic volatility (MSV) model in which factor covariance matrices are driven by Wishart random processes. The framework allows for unrestricted specification of intertemporal sensitivities, which can capture the persistence in volatilities, kurtosis in returns, and correlation breakdowns and contagion effects in volatilities. The factor structure allows addressing high dimensional setups used in portfolio analysis and risk management, as well as modeling conditional means and conditional variances within the model framework. Owing to the complexity of the model, we perform inference using Markov chain Monte Carlo simulation from the posterior distribution. A simulation study is carried out to demonstrate the efficiency of the estimation algorithm. We illustrate our model on a data set that includes 88 individual equity returns and the two Fama–French size and value factors. With this application, we demonstrate the ability of the model to address high dimensional applications suitable for asset allocation, risk management, and asset pricing.     

Factor Multivariate Stochastic Volatility via Wishart Processes

This paper proposes a high dimensional factor multivariate stochastic volatility (MSV) model in which factor covariance matrices are driven by Wishart random processes. The framework allows for unrestricted specification of intertemporal sensitivities, which can capture the persistence in volatilities, kurtosis in returns, and correlation breakdowns and contagion effects in volatilities. The factor structure allows addressing high dimensional setups used in portfolio analysis and risk management, as well as modeling conditional means and conditional variances within the model framework. Owing to the complexity of the model, we perform inference using Markov chain Monte Carlo simulation from the posterior distribution. A simulation study is carried out to demonstrate the efficiency of the estimation algorithm. We illustrate our model on a data set that includes 88 individual equity returns and the two Fama-French size and value factors. With this application, we demonstrate the ability of the model to address high dimensional applications suitable for asset allocation, risk management, and asset pricing.     

Inference for Lévy‐Driven Stochastic Volatility Models via Adaptive Sequential Monte Carlo

Abstract. We investigate simulation methodology for Bayesian inference in Lévy‐driven stochastic volatility (SV) models. Typically, Bayesian inference from such models is performed using Markov chain Monte Carlo (MCMC); this is often a challenging task. Sequential Monte Carlo (SMC) samplers are methods that can improve over MCMC; however, there are many user‐set parameters to specify. We develop a fully automated SMC algorithm, which substantially improves over the standard MCMC methods in the literature. To illustrate our methodology, we look at a model comprised of a Heston model with an independent, additive, variance gamma process in the returns equation. The driving gamma process can capture the stylized behaviour of many financial time series and a discretized version, fit in a Bayesian manner, has been found to be very useful for modelling equity data. We demonstrate that it is possible to draw exact inference, in the sense of no time‐discretization error, from the Bayesian SV model.     

中国短期利率跳跃行为的实证研究

内容提要：通过在Vasicek模型中引入跳跃强度与宏观经济变量相关的跳跃成分,本文建立了一个更具一般性的跳跃－扩散动态利率期限结构模型,并对该模型的五种不同形式进行了实证比较与分析。借助于新模型和比较结果,本文对中国短期利率的跳跃行为进行了实证研究。结果表明：（1）短期利率不仅存在均值回复和扩散行为,还存在显著的跳跃行为;（2）短期利率的跳跃强度存在显著的正向水平效应和宏观经济效应 ,但水平效应比宏观经济效应更显著;（3）跳跃行为、跳跃强度的水平效应以及宏观经济效应在刻画利率动态行为时都是必要的,现有的跳跃－扩散模型不足以描述中国短期利率的动态行为特征;（4）随着跳跃、跳跃强度的宏观经济效应和水平效应的逐步引入,模型的拟合优度和预测能力逐步显著提高。