Information in the Term Structure of Yield Curve Volatility

Using a novel no‐arbitrage model and extensive second‐moment data, we decompose conditional volatility of U.S. Treasury yields into volatilities of short‐rate expectations and term premia. Short‐rate expectations become more volatile than premia before recessions and during asset market distress. Correlation between shocks to premia and shocks to short‐rate expectations is close to zero on average and varies with the monetary policy stance. While Treasuries are nearly unexposed to variance shocks, investors pay a premium for hedging variance risk with derivatives. We illustrate the dynamics of the yield volatility components during and after the financial crisis.     

Interest Rate Volatility and the Term Structure: A Two-Factor General Equilibrium Model

We develop a two-factor general equilibrium model of the term structure. The factors are the short-term interest rate and the volatility of the short-term interest rate. We derive closed-form expressions for discount bonds and study the properties of the term structure implied by the model. The dependence of yields on volatility allows the model to capture many observed properties of the term structure. We also derive closed-form expressions for discount bond options. We use Hansen's generalized method of moments framework to test the cross-sectional restrictions imposed by the model. The tests support the two-factor model.     

Expectations Hypothesis of the Term Structure of Implied Volatility: Evidence from Foreign Currency and Stock Index Options

Using a stochastic volatility option pricing model, we showthat the implied volatilities of at-the-money options are notnecessarily unbiased and that the fixed interval time-seriescan produce misleading results. Our results do not support theexpectations hypothesis: long-term volatilities rise relativeto short-term volatilities, but the increases are not matchedas predicted by the expectations hypothesis. In addition, anincrease in the current long-term volatility relative to thecurrent short-term volatility is followed by a subsequent decline.The results are similar for both foreign currency and the S&P500 stock index options.     

基于贝塞尔曲线的中、美、日利率期限结构静态研究

利率期限结构曲线的静态拟合是指,使用不同类型的数学函数近似地描述整条利率期限结构曲线。当前最流行的静态拟合方法是利用B样条曲线来拟合利率曲线。然而,该方法往往受制于阶数的限制,而仅仅停留在3阶。本文通过利用B样条曲线的特殊形式——Bezier曲线拟合了中国、美国、日本国债利率的期限结构曲线,获得了一种可以升阶的拟合方法。同时,将复杂的曲线拟合计算,简化为对散点的聚类分析,取得了中国利率期限结构的模型。     

确定波动率的欧式期权鞅定价与利率期限结构

把merton随机利率期权模型扩展到允许基础资产支付红利情形,在一系列假设前提基础上重新运用鞅测度方法可以得到无套利时随机利率下欧式未定权益的一般定价公式,进而得出欧式期权定价的解析表达式。通过对债券价格过程的假设,构造出一个关于确定波动率的债券价格过程、单因素利率期限结构模型和债券价格之间的对应关系的命题,并由此得出了债券期权定价的解析公式。     

人民币汇率波动与我国通胀、产出波动：一个扩展泰勒曲线的研究

发挥市场供求对汇率的调节作用,增强人民币汇率双向浮动弹性,是当前我国汇率体制改革的主要方向。本文在泰勒曲线的框架下考察人民币汇率波动对我国宏观经济波动和货币政策实施的影响。通过实证研究发现,1994—2006年通货膨胀波动对人民币汇率波动是不敏感的,人民币汇率传递效应不显著,人民币汇率波动对宏观经济波动没有显著的影响;2007年以后人民币汇率波动推动泰勒曲线向内移动,因此更大的人民币汇率弹性对货币政策传导和货币政策有效性是有利的,逐步扩大的人民币汇率弹性区间对我国宏观经济运行是适宜和可接受的。另外人民币汇率波动也使得泰勒曲线更加陡峭,稳定通货膨胀所导致的产出缺口波动减小了,因而更有利于货币政策当局追求一个低而稳定的通胀目标。     

Identifying Monetary Policy Shocks via Changes in Volatility

A central issue of monetary policy analysis is the specification of monetary policy shocks. In a structural vector autoregressive setting there has been some controversy about which restrictions to use for identifying the shocks because standard theories do not provide enough information to fully identify monetary policy shocks. In fact, to compare different theories it would even be desirable to have over-identifying restrictions that would make statistical tests of different theories possible. It is pointed out that some progress toward over-identifying monetary policy shocks can be made by using specific data properties. In particular, it is shown that changes in the volatility of the shocks can be used for identification. Based on monthly U.S. data from 1965 to 1996 different theories are tested and it is found that associating monetary policy shocks with shocks to nonborrowed reserves leads to a particularly strong rejection of the model whereas assuming that the Fed accommodates demand shocks to total reserves cannot be rejected.     

人口学特征与利率期限结构:老年社会平缓的收益率曲线

本文将刻画人口结构的生命周期模型引入消费-资本资产定价模型,考察人口结构对利率期限结构的影响。模型表明,人口结构及其家庭生命周期特征不仅决定利率水平,而且将通过人对债券期限的不同偏好,影响利率期限结构。少年人口占比对利率期限结构的影响为正,中年和老年人口占比的影响为负。相比少年人口,中老年人口更偏好长期债券,使长期收益率下降,期限结构的斜率更为平缓。基于全球数据的经验研究验证了这一结论。少年人口占比增加期限利差,中老年人口占比则起反向作用。因此,在年长的经济体中,期限利差更小,呈现更平缓的收益率曲线特征。在更换人口结构变量、期限利差变量、估计方法、赋权样本和处理遗漏变量后,结果表现稳健。本文从人口学视角拓宽了利率期限结构的决定因素,揭示了老年经济体可能面临一个平缓的收益率曲线,而这说明老龄化还可能通过抑制短期投机和促进长期投资来提高长期经济发展质量。     

Term Structure Models: A Perspective from the Long Rate

Term structure models based on dynamic asset-pricing theory are discussed by taking a perspective from the long rate. This paper partially answers two questions about the asymptotic behavior of yields on default-free zero-coupon bonds: in frictionless markets having no arbitrage, what should the behavior be; and, in known term structure models, what can the behavior be.

In frictionless markets having no arbitrage, yields of all maturities should be positive and uniformly bounded from above. The yield curve should level out as term to maturity increases. Slopes with large absolute values occur only in the early maturities. In a continuous-time framework, the longer the maturity of the yield is, the less volatile it will be. The long rate should be a nondecreasing process. Furthermore, the long rate in continuous-time factor models with nonsingular volatility matrices should be a nondecreasing deterministic function.

In the Black, Derman, and Toy model and factor models with the short rate having the mean reversion property, yields of all maturities are uniformly bounded from above. The long rate in the Duffie and Kan model with the mean reversion property is a constant. The long rate in the Heath, Jarrow, and Morton model can be infinite or a nondecreasing process. Examples with the long rate increasing are given in this paper. A model with the long rate and short rate as two state variables is then obtained.     

中国国债收益率曲线的构造--基于利率期限结构的实证研究

国债收益率曲线即描述各种到期时间的国债收益率的图形,其研究思路为:首先设计一个能够在形式上符合我国利率期限结构特征的研究模型,然后根据商业银行存款利率,得出商业银行存款利率期限结构模型,之后研究回购利率的期限结构特征,并恰当地建模,最后利用商业银行存款利率模型和回购利率模型,结合国债定价,得到交易所国债的利率期限结构.     

Stochastic Volatility in a Macro-Finance Model of the U.S. Term Structure of Interest Rates 1961–2004

This paper generalizes the standard homoscedastic macro-finance model by allowing for stochastic volatility, using the "square root" specification of the mainstream finance literature. Empirically, this specification dominates the standard model because it is consistent with the square root volatility found in macroeconomic time series. Thus it establishes an important connection between the stochastic volatility of the mainstream finance model and macro-economic volatility of the Okun–Friedman type. This research opens the way to a richer specification of both macro-economic and term structure models, incorporating the best features of both macro-finance and mainstream finance models.     

Market Structure and Return Volatility: Evidence from the Hong Kong Stock Market

There is no consensus about the cause for higher volatility at the market open than at the market close in the U.S. market. As an order–driven, nonspecialist market, the Hong Kong stock market provides a useful setting for an examination. If halt of trade were the major cause of higher open–to–open volatility, the open–to–open volatility in the Hong Kong market would be higher. However, this is not observed. The autocorrelation of the open–to–open return series also indicates that the temporary price deviation at the market opening is not significant. We view these findings as consistent with the specialist argument.     

债务到期结构的影响因素：理论和证据

从个别简单分析和逐步回归法分析结果可知,市场价值/账面价值、公司规模、固定资产比例和加权平均资产期限显著地影响中国上市公司债务到期结构.     

Time Varying Term Premia and Traditional Hypotheses about the Term Structure

Empirical evidence of time varying term premia in bond returns is frequently interpreted as evidence against the Expectations Hypothesis. This paper shows that the Expectations Hypothesis can actually imply time varying term premia if the time frame for which the Expectations Hypothesis holds differs from the return measurement period. Furthermore, many of the properties of these term premia are consistent with those of observed term premia. These results are important because they imply that the case against the Expectations Hypothesis is weaker than claimed in the empirical literature.     

掉期曲线变动加剧,波动率期限结构扁平化——2019年人民币外汇衍生品市场回顾与展望

2019年人民币外汇掉期曲线形态变动非常之大,大方向上保持震荡上行,中美利差的变化是核心影响因素;而人民币期权波动率走势主要受中美贸易战影响,期限结构扁平化。展望2020年,由于中美利差有望震荡走低,但波幅及方向性将明显减弱,掉期市场可能会陷入窄幅盘整;随着中美贸易争端缓解,人民币期权波动率或于上半年底部震荡、下半年上扬。     

Testing Term Structure Estimation Methods: Evidence from the UK STRIPS Market

Prices and yields of UK government zero‐coupon bonds are used to test alternative yield curve estimation models. Zero‐coupon bonds permit a more pure comparison, as the models are providing only the interpolation service and also not making estimation feasible. It is found that better yield curves estimates are obtained by fitting to the yield curve directly rather than fitting first to the discount function. A simple procedure to set the smoothness of the fitted curves is developed, and a positive relationship between over‐smoothness and the fitting error is identified. A cubic spline function fitted directly to the yield curve provides the best overall balance of fitting error and smoothness, both along the yield curve and within local maturity regions.     

债务期限结构理论综述

企业的债务期限结构与企业价值是密切相关的。为此,一些经济学家对企业的债务期限结构进行了研究。这些研究成果大体上可以分为基于契约成本的理论、基于信息不对称的理论、基于税收的理论和基于期限匹配的理论。     

New Keynesian Macroeconomics and the Term Structure

This article complements the structural New Keynesian macro framework with a no-arbitrage affine term structure model. Whereas our methodology is general, we focus on an extended macro model with unobservable processes for the inflation target and the natural rate of output that are filtered from macro and term structure data. We find that term structure information helps generate large and significant parameters governing the monetary policy transmission mechanism. Our model also delivers strong contemporaneous responses of the entire term structure to various macroeconomic shocks. The inflation target shock dominates the variation in the "level factor" whereas monetary policy shocks dominate the variation in the "slope and curvature factors."     

Switching VARMA Term Structure Models

The purpose of this article is to propose a global discrete-timemodeling of the term structure of interest rates which is ableto capture simultaneously the following important features:(i) a historical dynamics of the factor driving term structureshapes involving several lagged values, and switching regimes;(ii) a specification of the stochastic discount factor (SDF)with time-varying and regime-dependent risk-premia; (iii) explicitor quasi explicit formulas for zero-coupon bond (ZCB) and interestrate derivative prices. We develop the switching autoregressivenormal (SARN) and the switching vector autoregressive normal(SVARN) Factor-Based Term Structure Models of order p. The factoris considered as a latent variable or an observable variable:in the second case the factor is a vector of several yields.Regime shifts are described by a Markov chain with (historical)nonhomogeneous transition probabilities. An empirical analysisof bivariate VAR(p) and SVARN(p) Factor-Based Term StructureModels, using monthly observations of the U.S. term structureof interest rates, and a goodness-of-fit and expectation hypothesispuzzle comparison with competing models in the literature, showsthe determinant role played by the observable nature of thefactor, lags, and switching regimes in the term structure modeling.     

Alternative Defaultable Term Structure Models

The objective of this paper is to consider defaultable term structure models in a general setting beyond standard risk-neutral models. Using as numeraire the growth optimal portfolio, defaultable interest rate derivatives are priced under the real-world probability measure. Therefore, the existence of an equivalent risk-neutral probability measure is not required. In particular, the real-world dynamics of the instantaneous defaultable forward rates under a jump-diffusion extension of a HJM type framework are derived. Thus, by establishing a modelling framework fully under the real-world probability measure, the challenge of reconciling real-world and risk-neutral probabilities of default is deliberately avoided, which provides significant extra modelling freedom. In addition, for certain volatility specifications, finite dimensional Markovian defaultable term structure models are derived. The paper also demonstrates an alternative defaultable term structure model. It provides tractable expressions for the prices of defaultable derivatives under the assumption of independence between the discounted growth optimal portfolio and the default-adjusted short rate. These expressions are then used in a more general model as control variates for Monte Carlo simulations of credit derivatives. Nicola Bruti-Liberati: In memory of our beloved friend and colleague.