Foreign Exchange Intervention by the Bank of Japan: Bayesian Analysis Using a Bivariate Stochastic Volatility Model

A bivariate stochastic volatility model is employed to measure the effect of intervention by the Bank of Japan (BOJ) on daily returns and volume in the USD/YEN foreign exchange market. Missing observations are accounted for, and a data-based Wishart prior for the precision matrix of the errors to the transition equation that is in line with the likelihood is suggested. Empirical results suggest there is strong conditional heteroskedasticity in the mean-corrected volume measure, as well as contemporaneous correlation in the errors to both the observation and transition equations. A threshold model is used for the BOJ reaction function, which is estimated jointly with the bivariate stochastic volatility model via Markov chain Monte Carlo. This accounts for endogeneity between volatility in the market and the BOJ reaction function, something that has hindered much previous empirical analysis in the literature on central bank intervention. The empirical results suggest there was a shift in behavior by the BOJ, with a movement away from a policy of market stabilization and toward a role of support for domestic monetary policy objectives. Throughout, we observe “leaning against the wind” behavior, something that is a feature of most previous empirical analysis of central bank intervention. A comparison with a bivariate EGARCH model suggests that the bivariate stochastic volatility model produces estimates that better capture spikes in in-sample volatility. This is important in improving estimates of a central bank reaction function because it is at these periods of high daily volatility that central banks more frequently intervene.     

Estimation of the Stochastic Volatility Model by the Empirical Characteristic Function Method

The stochastic volatility model has no closed form for its likelihood and hence the maximum likelihood estimation method is difficult to implement. However, it can be shown that the model has a known characteristic function. As a consequence, the model is estimable via the empirical characteristic function. In this paper, the characteristic function of the model is derived and the estimation procedure is discussed. An application is considered for daily returns of Australian/New Zealand dollar exchange rate. Model checking suggests that the stochastic volatility model together with the empirical characteristic function estimates fit the data well.     

SABR随机波动率LIBOR市场模型的参数校准估计方法与实证模拟

针对标准化Libor市场模型（LMM）和Heston随机波动率Libor市场模型（Heston-LMM）的应用局限,首先将SABR代替Heston过程引入标准化Libor市场模型框架,建立非标准化的SABR随机波动率Libor市场模型（SABR-LMM）;在此基础上,运用利率上限期权（Cap）、利率互换期权（Swaption）和自适应马尔科夫链蒙特卡罗模拟方法（MCMC）对模型参数进行有效市场校准与模拟估计;最后,针对三个月美元Libor远期利率实际数据,对上述三类Libor市场模型的实际运行效果进行了实证模拟计算与比较分析。研究结论认为,基于模拟利差计算结果,针对短期Libor利率模拟而言,与LMM和Heston -LMM两类模型而言,加入SABR波动项的SABR-LMM模型具有更小的模拟误差,因而具有更好的模拟效果。     

An empirical analysis of the volatility of the Japanese stock price index: a non-parametric approach

This paper presents an empirical analysis of stochastic features of volatility in the Japanese stock price index, or TOPIX, using high-frequency data sampled every 5 min. The process of TOPIX is modeled by a stochastic differential equation with the time-homogeneous drift and diffusion coefficients. To avoid the risk of misspecification for the volatility function, which is defined by the squared diffusion coefficient, the local polynomial model is applied to the data, and then produced the estimates of the volatility function together with their confidence intervals. The result of the estimation suggests that the volatility function shows similar patterns for one period, but drastically changes for another.     

SVJD-LIBOR随机动态模型的市场校准估计与实证模拟

针对跳跃扩散LIBOR市场模型（JD-LIBOR）与随机波动率LIBOR市场模型（SVJD-LMM）各自应用局限,首先将正态跳跃扩散与Heston随机波动率同时引入标准化LIBOR市场模型中,建立一类新型双重驱动非标准化LIBOR市场模型（SVJD-LMM）。其次,运用Cap、Swaption等利率衍生产品市场数据和Black逆推校准方法,对模型的局部波动参数与瞬间相关性参数进行有效市场校准;并运用自适应马尔科夫链蒙特卡罗模拟方法（此后简称A-MCMC）对模型的随机波动率、跳跃扩散等其他主要参数进行有效理论估计与实证模拟。最后,针对六月期美元Libor远期利率实际数据,对上述三类市场模型进行了模拟比较分析。研究结论认为,若在单因子Libor利率市场模型基础上引入跳跃扩散过程,并且联立波动率的随机微分方程,则可极大地提高利率模型的解释力;加入随机波动率和跳跃扩散过程的模拟计算结果与实际利率的误差更小,从而更接近现实情况。     

Derivative Pricing With Wishart Multivariate Stochastic Volatility

This paper deals with the pricing of derivatives written on several underlying assets or factors satisfying a multivariate model with Wishart stochastic volatility matrix. This multivariate stochastic volatility model leads to a closed-form solution for the conditional Laplace transform, and quasi-explicit solutions for derivative prices written on more than one asset or underlying factor. Two examples are presented: (i) a multiasset extension of the stochastic volatility model introduced by Heston (1993), and (ii) a model for credit risk analysis that extends the model of Merton (1974) to a framework with stochastic firm liability, stochastic volatility, and several firms. A bivariate version of the stochastic volatility model is estimated using stock prices and moment conditions derived from the joint unconditional Laplace transform of the stock returns.     

Long memory stochastic volatility : A bayesian approach

We propose a simulation-based Bayesian approach to the analysis of long memory stochastic volatility models, stationary and nonstationary. The main tool used to reduce the likelihood function to a tractable form is an approximate state-space representation of the model, A data set of stock market returns is analyzed with the proposed method. The approach taken here allows a quantitative assessment of the empirical evidence in favor of the stationarity, or nonstationarity, of the instantaneous volatility of the data.     

Asymmetric Multivariate Stochastic Volatility

This paper proposes and analyses two types of asymmetric multivariate stochastic volatility (SV) models, namely, (i) the SV with leverage (SV-L) model, which is based on the negative correlation between the innovations in the returns and volatility, and (ii) the SV with leverage and size effect (SV-LSE) model, which is based on the signs and magnitude of the returns. The paper derives the state space form for the logarithm of the squared returns, which follow the multivariate SV-L model, and develops estimation methods for the multivariate SV-L and SV-LSE models based on the Monte Carlo likelihood (MCL) approach. The empirical results show that the multivariate SV-LSE model fits the bivariate and trivariate returns of the S&P 500, the Nikkei 225, and the Hang Seng indexes with respect to AIC and BIC more accurately than does the multivariate SV-L model. Moreover, the empirical results suggest that the univariate models should be rejected in favor of their bivariate and trivariate counterparts.     

Asymmetric Multivariate Stochastic Volatility

This paper proposes and analyses two types of asymmetric multivariate stochastic volatility (SV) models, namely, (i) the SV with leverage (SV-L) model, which is based on the negative correlation between the innovations in the returns and volatility, and (ii) the SV with leverage and size effect (SV-LSE) model, which is based on the signs and magnitude of the returns. The paper derives the state space form for the logarithm of the squared returns, which follow the multivariate SV-L model, and develops estimation methods for the multivariate SV-L and SV-LSE models based on the Monte Carlo likelihood (MCL) approach. The empirical results show that the multivariate SV-LSE model fits the bivariate and trivariate returns of the S&P 500, the Nikkei 225, and the Hang Seng indexes with respect to AIC and BIC more accurately than does the multivariate SV-L model. Moreover, the empirical results suggest that the univariate models should be rejected in favor of their bivariate and trivariate counterparts.     

INDEX TO VOLUME 4 (1986)

This article provides an empirical investigation of the risk-neutral variance process and the market price of variance risk implied in the foreign-currency options market. There are three principal contributions. First, the parameters of Heston's mean-reverting square-root stochastic volatility model are estimated using dollar/mark option prices from 1987 to 1992. Second, it is shown that these implied parameters can be combined with historical moments of the dollar/mark exchange rate to deduce an estimate of the market price of variance risk. These estimates are found to be nonzero, time varying, and of sufficient magnitude to imply that the compensation for variance risk is a significant component of the risk premia in the currency market. Finally, the out-of-sample test suggests that the historical variance and the Hull and White implied variance contain no more information than that imbedded in the Heston implied variance.     

随机波动HJM框架下信用利差模型及实证研究

将随机波动引入到具有违约风险的HJM模型中,基于无套利条件推导得出随机波动HJM模型框架下信用利差的漂移项限制条件,从而构建了随机波动HJM框架下的信用利差模型,并基于波动率结构的适当设定对模型进行马尔科夫简化,进而利用该模型对中国可违约债券市场信用利差的动态特性进行实证分析。结果发现：短期信用利差的动态特性具有显著的随机波动特征,而随机波动HJM框架下的信用利差模型可以很好地刻画中国可违约债券市场信用利差的动态特性。     

基于拟似然方法的股票收益与波动率关系及其应用研究

股票市场中收益与波动率的关系研究在金融证券领域起着很重要的作用,而随机波动率模型能够很好地拟合这种关系。本文将拟似然方法和渐近拟似然方法运用在随机波动率模型的参数估计方面,渐近拟似然方法可以避免因为人为的结构错误指定而造成的偏差,比较稳健。本文采用拟似然和渐近拟似然方法对随机波动率模型的参数估计进行了模拟探索,并和两种已有估计方法进行了对比,结果表明拟似然和渐近拟似然方法在模型的参数估计方面有着很好的估计结果。实证研究中,选取2000-2015年标普500指数作为研究对象,结果显示所选数据具有金融时间序列的常见特征。本文为金融证券领域中股票收益与波动率关系及其应用研究提供了一定的启示。     

Comparing volatility forecasting models during the global financial crisis

Volatility estimation in financial markets has always been a challenge especially in time of crisis. Once asset prices and investment decisions are highly sensitive to such variable, many different models have been proposed in literature. This article estimates the volatility from a new family of stochastic volatility models called non-Gaussian State Space Models, a subclass of state space models where it is possible to compute exact likelihood. Volatilities of important Asian and Oceanian stock market indexes have been estimated and compared to APARCH model estimates. Results showed that non-Gaussian State Space Models outperformed significantly in both in-sample and forecasting cases.     

Likelihood-Based comparison of stable paretian and competing models: Evidence from daily exchange rates

Considering alternative models for exchange rates has always been a central issue in applied research. Despite this fact, formal likelihood-based comparisons of competing models are extremely rare. In this paper, we apply the Bayesian marginal likelihood concept to compare GARCH, stable, stable GARCH, stochastic volatility, and a new stable Paretian stochastic volatility model for seven major currencies. Inference is based on combining Monte Carlo methods with Laplace integration. The empirical results show that neither GARCH nor stable models are clear winners, and a GARCH model with stable innovations is the model best supported by the data.     

Monte Carlo Maximum Likelihood Estimation for Generalized Long-Memory Time Series Models

An exact maximum likelihood method is developed for the estimation of parameters in a non-Gaussian nonlinear density function that depends on a latent Gaussian dynamic process with long-memory properties. Our method relies on the method of importance sampling and on a linear Gaussian approximating model from which the latent process can be simulated. Given the presence of a latent long-memory process, we require a modification of the importance sampling technique. In particular, the long-memory process needs to be approximated by a finite dynamic linear process. Two possible approximations are discussed and are compared with each other. We show that an autoregression obtained from minimizing mean squared prediction errors leads to an effective and feasible method. In our empirical study, we analyze ten daily log-return series from the S&P 500 stock index by univariate and multivariate long-memory stochastic volatility models. We compare the in-sample and out-of-sample performance of a number of models within the class of long-memory stochastic volatility models.     

Monte Carlo Likelihood Estimation for Three Multivariate Stochastic Volatility Models

Estimating parameters in a stochastic volatility (SV) model is a challenging task. Among other estimation methods and approaches, efficient simulation methods based on importance sampling have been developed for the Monte Carlo maximum likelihood estimation of univariate SV models. This paper shows that importance sampling methods can be used in a general multivariate SV setting. The sampling methods are computationally efficient. To illustrate the versatility of this approach, three different multivariate stochastic volatility models are estimated for a standard data set. The empirical results are compared to those from earlier studies in the literature. Monte Carlo simulation experiments, based on parameter estimates from the standard data set, are used to show the effectiveness of the importance sampling methods.     

非对称随机波动模型在中国股市的应用

为了探测随机波动模型的非对称特征,修改传统的随机波动模型建立非对称的随机波动模型,采用基于马尔可夫链蒙特卡洛(MCMC)模拟的贝叶斯分析对模型进行参数估计。对中国深圳、上海股市波动进行实证研究发现,非对称随机波动模型能较好地探测波动存在的非对称波动。与GJR-GARCH模型相比,非对称随机波动模型预测效果更好。     

Monte Carlo Likelihood Estimation for Three Multivariate Stochastic Volatility Models

Estimating parameters in a stochastic volatility (SV) model is a challenging task. Among other estimation methods and approaches, efficient simulation methods based on importance sampling have been developed for the Monte Carlo maximum likelihood estimation of univariate SV models. This paper shows that importance sampling methods can be used in a general multivariate SV setting. The sampling methods are computationally efficient. To illustrate the versatility of this approach, three different multivariate stochastic volatility models are estimated for a standard data set. The empirical results are compared to those from earlier studies in the literature. Monte Carlo simulation experiments, based on parameter estimates from the standard data set, are used to show the effectiveness of the importance sampling methods.     

Evaluation of realized volatility predictions from models with leptokurtically and asymmetrically distributed forecast errors

Accurate volatility forecasting is a key determinant for portfolio management, risk management and economic policy. The paper provides evidence that the sum of squared standardized forecast errors is a reliable measure for model evaluation when the predicted variable is the intra-day realized volatility. The forecasting evaluation is valid for standardized forecast errors with leptokurtic distribution as well as with leptokurtic and asymmetric distributions. Additionally, the widely applied forecasting evaluation function, the predicted mean-squared error, fails to select the adequate model in the case of models with residuals that are leptokurtically and asymmetrically distributed. Hence, the realized volatility forecasting evaluation should be based on the standardized forecast errors instead of their unstandardized version.