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。     

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。     

跳跃扩散利率期限结构模型的MCMC法估计

近来的实证研究表明:在通常的利率扩散过程中加入跳跃项后能更好地解释利率的动态行为。本文使用马尔可夫链蒙特卡罗方法,研究我国的动态利率期限结构,数据为银行间同业拆借市场7天拆借利率(CHIBOR07)的月度数据,样本区间为1997/01—2006/02。我们得出了没有引入跳跃的模型可能存在模型误设问题,引入跳跃后的模型能对经验数据(CHIBOR07)提供更好的解释的结论。     

高频数据驱动的连续时间模型估计

现代金融经济学中连续时间模型能够更方便地描述重要经济变量的动态过程如股价、汇率和利率等。为连续时间模型提出了一种高频数据驱动的二阶段估计方法,增强了连续时间扩展模型的弹性和可操作性。以Vasicek模型为例给出了该方法的应用实例,首先在第一阶段使用实现波动率方法估计出模型的扩散项参数,然后使用实际数据的稳态分布的前向方程估计漂移项参数。此方法对模型初始设定和优化算法依赖程度低,结果较为稳定可靠。     

基于跳跃-扩散模型的短期市场利率研究

当跳跃-扩散过程被引入利率期限结构研究之后,一直成为焦点和热点问题。如何对跳跃-扩散过程进行参数拟合是很重要的问题,本文拟在前面的基础上对扩散过程的短期利率作出进一步的研究,希望提出一个新的方法,更好的为我短期利率模型拟合出比较优越的参数。     

资本配置摩擦与中国经常项目波动

本文将国内资本市场摩擦和国际资本流动摩擦引入RBC模型,并采用贝叶斯方法校准模拟了中国经常项目的波动轨迹。研究结果表明：（1）国内资本市场摩擦和国际资本流动摩擦是形成中国经常项目波动的重要传导机制,两类资本市场摩擦机制的引入有助于准确拟合中国经常项目波动的波动性、协动性和持续性等各项特征;（2）贝叶斯估计得到的中国的资本调整成本和利率风险利差的参数值反映了中国资本配置效率和国际资本流动程度介于其他新兴市场经济体和发达经济体的水平之间;（3）中国经常项目波动主要由利率变动冲击和偏好冲击等两类结构性外生冲击通过国内资本市场摩擦机制和国际资本流动摩擦机制传导形成。     

交易信息、跳跃发现与波动率估计

在高频金融数据研究中,估计金融资产价格序列积分波动率时,往往需要考虑市场微观结构噪声与资产价格跳跃的影响.本文将市场微观结构噪声部分地表示成交易信息的参数函数,并结合资产收益序列的跳跃特征,提出资产收益的高斯混合模型.本文利用EM算法进行噪声参数估计的同时,识别资产价格的跳跃,进而提出一种新的积分波动率的估计量.本文提出的方法可以视为Li等(2016)的改进,并在模拟研究中,得到了比Li等(2016)更好的参数估计效果,且即使在跳跃幅度分布误设的情况下,也具有良好的识别跳跃的功能.在应用举例中,对比了本文方法与Lee和Mykland(2008)的跳跃发现方法,论证了本文的模型在识别跳跃方面的可靠性.     

金融市场波动跳跃、跳跃相依与跳跃风险:基于股指高频数据的研究

运用股指高频数据,首先构建基于一般已实现波动率与双幂次变差的RV-regular vine copula模型,比较分析两个模型在刻画资本市场之间的波动跳跃结构的差异;然后,考虑股票价格存在跳跃的情形,分析离散跳跃的统计特征,研究资本市场之间跳跃相依结构,并通过模拟计算市场在险价值来探讨市场之间的跳跃相依风险。研究发现:由于跳跃的存在,采用双幂次变差所构建的RV-regular vine copula模型在参数估计结果方面表现更佳;跳跃序列存在尖峰厚尾的特征以及跳跃聚集的现象,而跳跃相依风险可以通过构建合适的资产组合来降低。     

中国资产价格跳跃行为研究——基于高频数据集的分析

利用日内高频数据,分别通过实现波动率模型和实现二次幂波动模型对资产价格的波动率和连续部分波动率建模,并据此得到资产价格跳跃部分的动态行为模型,分离出发生跳跃的天数、跳跃的大小和方向。结果显示,中国金融市场中的资产跳跃行为密集发生在市场波动性较大的时刻,其大小和间隔期均具有群聚现象,且五种代表性资产价格的跳跃密度均呈左偏分布,说明中国股权市场中向下发生的跳跃多于向上的跳跃。     

汇率市场、利率市场与金属期货动态关联的实证

文章利用前期残差标准化后构成的方差系数,构建动态相关条件的多位广义ARCH模型,研究按照铁矿金属期货与汇率市场、货币市场间条件关联的验证分析,进行残差的预估,并按照标准化后的LME及其残差序列、汇率、利率进行x2分布的动态条件检验.结果显示:铁金属期货的期货市场自身以及外汇、利率市场波动呈现显著的集聚参数特征,而各国货币政策对于这一联动变化影响也形成显著的利差变化关联.     

HEAVY-TAILED-DISTRIBUTED THRESHOLD STOCHASTIC VOLATILITY MODELS IN FINANCIAL TIME SERIES

To capture mean and variance asymmetries and time‐varying volatility in financial time series, we generalize the threshold stochastic volatility (THSV) model and incorporate a heavy‐tailed error distribution. Unlike existing stochastic volatility models, this model simultaneously accounts for uncertainty in the unobserved threshold value and in the time‐delay parameter. Self‐exciting and exogenous threshold variables are considered to investigate the impact of a number of market news variables on volatility changes. Adopting a Bayesian approach, we use Markov chain Monte Carlo methods to estimate all unknown parameters and latent variables. A simulation experiment demonstrates good estimation performance for reasonable sample sizes. In a study of two international financial market indices, we consider two variants of the generalized THSV model, with US market news as the threshold variable. Finally, we compare models using Bayesian forecasting in a value‐at‐risk (VaR) study. The results show that our proposed model can generate more accurate VaR forecasts than can standard models.     

Bayesian inference for Heston-STAR models

The Heston-STAR model is a new class of stochastic volatility models defined by generalizing the Heston model to allow the volatility of the volatility process as well as the correlation between asset log-returns and variance shocks to change across different regimes via smooth transition autoregressive (STAR) functions. The form of the STAR functions is very flexible, much more so than the functions introduced in Jones (J Econom 116:181–224, 2003), and provides the framework for a wide range of stochastic volatility models. A Bayesian inference approach using data augmentation techniques is used for the parameters of our model. We also explore goodness of fit of our Heston-STAR model. Our analysis of the S&P 500 and VIX index demonstrates that the Heston-STAR model is more capable of dealing with large market fluctuations (such as in 2008) compared to the standard Heston model.     

上证指数收益率的特征及其波动性分析

股票价格的频繁波动是股票市场最明显的特征之一。ARCH类模型可以很好地预测金融资产收益率的方差。通过对上证指数的统计分析表明,上证指数的收益率分布表现出非正态性,并存在自回归条件异方差的特征。利用ARCH类模型对上证指数的波动进行了拟合,结果表明GARCH(1,1)模型对上证指数波动具有较好的拟合效果。     

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.     

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.     

Inference for a Class of Stochastic Volatility Models Using Option and Spot Prices: Application of a Bivariate Kalman Filter

In this paper Bayesian methods are applied to a stochastic volatility model using both the prices of the asset and the prices of options written on the asset. Posterior densities for all model parameters, latent volatilities and the market price of volatility risk are produced via a Markov Chain Monte Carlo (MCMC) sampling algorithm. Candidate draws for the unobserved volatilities are obtained in blocks by applying the Kalman filter and simulation smoother to a linearization of a nonlinear state space representation of the model. Crucially, information from both the spot and option prices affects the draws via the specification of a bivariate measurement equation, with implied Black–Scholes volatilities used to proxy observed option prices in the candidate model. Alternative models nested within the Heston (1993) framework are ranked via posterior odds ratios, as well as via fit, predictive and hedging performance. The method is illustrated using Australian News Corporation spot and option price data.     

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。     

A Stochastic Simulation Approach to Model Selection for Stochastic Volatility Models

Stochastic volatility models have been widely appreciated in empirical finance such as option pricing, risk management, etc. Recent advances of Markov chain Monte Carlo (MCMC) techniques made it possible to fit all kinds of stochastic volatility models of increasing complexity within Bayesian framework. In this article, we propose a new Bayesian model selection procedure based on Bayes factor and a classical thermodynamic integration technique named path sampling to select an appropriate stochastic volatility model. The performance of the developed procedure is illustrated with an application to the daily pound/dollar exchange rates data set.