基于Hull-White模型的债券市场利率期限结构研究

现代利率研究中有许多理论和模型对利率期限结构问题进行探索，但是在中国还没有一种公认的理论或方法能够完全解决中国债券市场利率期限结构问题。本文尝试寻找一种更多的利用市场即时信息的定价方法对利率期限结构进行研究，应用三叉树模拟技术构建Hull-White模型，并对当前中国债券市场上几种常用利率进行比较分析。研究发现银行间质押式回购收益率具有较好的动态运动性质，比样本国债和政策性银行金融债更适宜作为短期金融产品定价的基础。     

利率期限结构与宏观经济变量的相互关系研究

本文研究了利率期限结构与宏观经济变量之间的相互关系。运用利率期限结构与宏观经济变量的无套利模型,对向量自回归模型进行了扩展,将其引入到状态空间模型框架中,基于卡尔曼滤波并结合EM算法对模型参数进行了有效估计,结合实际数据对利率期限结构与宏观经济变量的相互影响关系进行了实证研究。结果表明:利率期限结构与宏观经济变量的双向影响关系显著;宏观经济变量对利率期限结构具有一定的解释力;研究利率期限结构时,宏观经济变量的影响作用不能忽略。     

修正的FH利率期限结构模型

本文证明了在B.Flesaker和L.Hughston利率期限模型中的鞅性要求可以去掉，此外其模型构造方法可以推广到更一般情形，即从一个参考资产和一个市场风险价格构造利率期限结构。我们由此给出利率衍生证券的更一般定价公式。     

基于NS混合模型的中国利率期限结构动态估计比较研究

采用NS混合模型动态估计中国利率期限结构,考察动态NS模型,无套利NS模型及广义无套利NS模型等NS混合模型对我国利率期限结构的动态估计效率,比较NS混合模型的样本外预测能力,检验无套利约束对混合模型动态估计的影响.本文的经验分析结果表明:无套利条件的引入增强了NS混合模型的样本内动态估计能力和样本外预测能力;五因素的广义无套利NS模型(AFGNS)无论在利率期限结构样本内动态估计还是在总体预测效率上都要高于其他模型,可将其作为利率期限结构研究的基础模型:     

基于线性规划和多项式样条函数的利率期限结构模型

针对线形规划利率期限结构模型只能得到离散贴现率,提出利用多项式插值方法拟合出连续光滑的利率期限结构.并依据样本内外国债信息把它与多项式样条函数模型进行了实证比较,前者的价格相对误差分别为0.45%和1.51%,后者分别为4.18%和4.5%.结果表明线性规划利率期限结构模型与多项式插值相结合的方法在拟合我国利率期限结构方面具有一定优势.     

基于共轭几何变换程序的国债市场利率期限结构波动建模

本文变革已有的利率期限结构模型估计依赖于定价误差平方和最小化原则,引入几何双重变换程序解决非线性约束的误差绝对距离最小化问题,丰富国债市场利率波动和定价研究的理论体系和研究方法;运用负指数平滑立方L₁样条优化模型,克服B样条函数对节点数目与定位的过度敏感和放宽对贴现函数的二阶导数平滑要求,协同拟合误差绝对距离与贴现函数波动率最小化,保留B样条函数刻画中长期利率波动趋势的优势,增强对短期利率波动结构突变的估计、定价和预测能力,缓解B样条和NSS模型在利率期限结构拟合存在的过度波动问题。     

考虑流动性的我国国债价格预测研究

随着金融改革的深化和利率市场化脚步的加快,我国的国债交易和国债市场已经得到了高速发展和充分成长.但在国债利率期限结构的研究方面还不够充分,仍有进一步完善的空间,在利率期限结构研究中考虑流动性的影响就是其中之一.从利率期限结构估计入手,将流动性以权重形式加入NSS模型,估计参数并预测国债价格.研究结果表明,加入流动性权重后,利率期限结构的预测性能显著提高,而且随着步长加大,效果更明显.     

基于双因素利率期限结构模型的国债市场利率行为研究

本引用一种新的计量经济学方法-高斯估计法，通过Gauss语言编程，使用国债市场短期利率数据对双因素连续时间利率期限结构模型进行了参数估计和预测，得出的结果较理想，从而能更好的了解国债市场短期利率行为特点。     

基于预期理论的Shibor期限结构实证研究

本文基于利率期限结构预期理论对我国的Shibor市场进行了实证研究。本文回顾了利率期限结构预期理论的三种检验方法,通过单位根检验发现Shibor短端利率平稳、中长端利率存在单位根,并分别运用线性回归法、向量自回归法和协整检验法对Shibor整体、短端利率和中长端利率相应进行了实证检验,得出Shibor无论整体上还是短端利率或中长端利率都不支持预期理论成立的结论,并通过分析得出启示:Shibor应注重中长端利率的发展和报价制度的完善。     

国外同业拆借利率期限结构影响因素的实证分析——以美元LIBOR为例

通过选择反映经济的基本面和具体市场的资金面的变量建立不带移动平均项的自回归分布滞后模型,研究美元LIBOR期限结构影响因素,得到以下结论：从长期来看,通货膨胀率、联邦基金利率、道琼斯工业指数和广义货币的增长率都对LIBOR利率的水平值和斜率有影响．另外,水平值还受到三年期国债收益率的影响．从短期来看,影响水平值的因素有通货膨胀率和联邦基金利率,而三年期国债收益率是影响斜率的唯一短期因素．     

Heavy tail and light tail of Cox-Ingersoll-Ross processes with regime-switching

This study aims to investigate the tail behavior of Cox-Ingersoll-Ross(CIR) processes with regime switching. An essential difference shown in this study between CIR processes with and without regime switching is that the stationary distribution of those with regime switching may be heavy-tailed. We first provide sharp criteria to justify the existence of a stationary distribution for the CIR process with regime switching, which is applied to study the long-term returns of interest rates. Then, we provide a criterion to identify whether this distribution is heavy-tailed. Our results provide theoretical evidence of the existence of regime switching for interest-rate models based on empirical evidence of a heavy-tailed distribution.     

机制转换条件下股市收益率跳跃行为研究:基于RS-ARJI模型的以中国股市为例的实证分析

为检验股市收益率机制转换特性,考察机制转换条件下股市收益率的跳跃特征,以及在不同机制下跳跃行为对股市收益率的冲击效应,将Markov机制转换思想引入自回归跳跃(ARJI)模型,构建一个机制转换自回归跳跃(RS-ARM)模型.基于该模型对中国股市进行实证研究,结果表明:股市存在高、低波动两种机制,高波动时期的跳跃幅度和强度及其对股市收益率的冲击均大于低波动时期.同时,波动率估计和预测评价指标显示,RS-ARJI模型优于目前被广泛使用的GARCH模型和ARJI模型.     

Modeling dependence dynamics through copulas with regime switching

Measuring dynamic dependence between international financial markets has recently attracted great interest in financial econometrics because the observed correlations rose dramatically during the 2008–09 global financial crisis. Here, we propose a novel approach for measuring dependence dynamics. We include a hidden Markov chain (MC) in the equation describing dependence dynamics, allowing the unobserved time-varying dependence parameter to vary according to both a restricted ARMA process and an unobserved two-state MC. Estimation is carried out via the inference for the margins in conjunction with filtering/smoothing algorithms. We use block bootstrapping to estimate the covariance matrix of our estimators. Monte Carlo simulations compare the performance of regime switching and no switching models, supporting the regime-switching specification. Finally the proposed approach is applied to empirical data, through the study of the S&P500 (USA), FTSE100 (UK) and BOVESPA (Brazil) stock market indexes.     

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Brownian motion and normal distribution have been widely used in Cox-Ingersoll-Ross interest rate framework to model the instantaneous interest rate dynamics. However, empirical studies have also shown that the return distribution of interest rate has a higher peak and two fatter tails than those of the normal distribution. Meanwhile, when the rare catastrophic shocks occur or the regime shifts in the economy and finance, the money market may have jumps. In this paper, we will consider a class of reflected Cox-Ingersoll-Ross interest rate models with noise. Furthermore, we shall continue to supply the Laplace transform of the stationary distribution about this reflected diffusion process with jumps.     

信用风险相关性度量的MRS Copula模型构建及实证研究

在构建行业信用风险指数的基础上,将马尔科夫机制转换引入到信用风险相关性的度量中,建立了信用风险相关性度量的MRS Copula模型。以1990-2012年电力、煤气及水的生产和供应业,批发、零售、贸易业,石油、化学、塑胶、塑料业和信息技术业为样本的实证研究表明,行业信用风险相关性表现出较为明显的机制转换特征和非对称效应,在高风险状态,信用风险相关系数达到了0.7以上,而在低风险状态,信用风险相关系数在0.2以下.同时,信用风险"一损俱损"的特征比较明显,行业信用风险的下尾相关系数较为显著,而上尾相关系数则并不显著.商业银行可据此调整信贷资产结构,防范信用风险传染,以及优化信贷组合管理.     

Stochastic volatility Gaussian Heath-Jarrow-Morton models

This paper extends the class of deterministic volatility Heath-Jarrow-Morton models to a Markov chain stochastic volatility framework allowing for jump discontinuities and a variety of deformations of the term structure of forward rate volatilities. Analytical solutions for the dynamics of the volatility term structure are obtained. Semimartingale decompositions of the interest rates under a spot and forward martingale measures are identified. Stochastic volatility versions of the continuous time Ho-Lee and Hull-White extended Vasicek models are obtained. Introducing a regime shift in volatility that is an exponential function of time to maturity leads to a Vasicek dynamics with regime switching coefficients of the short rate.     

Risk Minimizing Option Pricing for a Class of Exotic Options in a Markov-Modulated Market

We address risk minimizing option pricing in a regime switching market where the floating interest rate depends on a finite state Markov process. The growth rate and the volatility of the stock also depend on the Markov process. Using the minimal martingale measure, we show that the locally risk minimizing prices for certain exotic options satisfy a system of Black-Scholes partial differential equations with appropriate boundary conditions. We find the corresponding hedging strategies and the residual risk. We develop suitable numerical methods to compute option prices.     

A fractional credit model with long range dependent default rate

Motivated by empirical evidence of long range dependence in macroeconomic variables like interest rates we propose a fractional Brownian motion driven model to describe the dynamics of the short and the default rate in a bond market. Aiming at results analogous to those for affine models we start with a bivariate fractional Vasicek model for short and default rate, which allows for fairly explicit calculations. We calculate the prices of corresponding defaultable zero-coupon bonds by invoking Wick calculus. Applying a Girsanov theorem we derive today’s prices of European calls and compare our results to the classical Brownian model.     

Numerical methods for backward Markov chain driven Black-Scholes option pricing

The drift, the risk-free interest rate, and the volatility change over time horizon in realistic financial world. These frustrations break the necessary assumptions in the Black-Scholes model (BSM) in which all parameters are assumed to be constant. To better model the real markets, a modified BSM is proposed for numerically evaluating options price-changeable parameters are allowed through the backward Markov regime switching. The method of fundamental solutions (MFS) is applied to solve the modified model and price a given option. A series of numerical simulations are provided to illustrate the effect of the changing market on option pricing.     

Risk Minimizing Option Pricing in a Regime Switching Market

Abstract

We study option pricing in a regime switching market where the risk free interest rate, growth rate and the volatility of a stock depends on a finite state Markov chain. Using a minimal martingale measure we show that the risk minimizing option price satisfies a system of Black–Scholes partial differential equations with weak coupling.