Analysis of Multifactor Affine Yield Curve Models
Analysis of Multifactor Affine Yield Curve Models
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DOI：
10.1198/jasa.2009.ap08029
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发表时间：
2009-12
影响因子：
3.7
通讯作者：
S. Chib;Bakhodir A. Ergashev
中科院分区：
文献类型：
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作者：
S. Chib;Bakhodir A. Ergashev
在金融学和经济学中，人们对收益率曲线的理论建模和统计估计做了大量的工作，收益率曲线被定义为（−1/τ）log pt（τ）和τ之间的关系，其中pt（τ）是到期日t+τ时收益为1的零息债券在时间t的价格。当前人们非常感兴趣的是收益率曲线模型，在该模型中，一组观察到的和潜在的因素决定了要素风险的市场价格、随机贴现因子和无套利债券价格。从统计学的角度来看，该模型特别有趣，因为产量是基础参数的复杂非线性函数（例如，出现在因素的演化动态中的那些和出现在因素风险的模型中的那些）。这种非线性倾向于产生多峰的似然函数。在这篇文章中，我们将重新讨论如何从贝叶斯观点来拟合这些模型。推理框架的主要方面包括：（a）模型参数的先验，其动机是经济考虑，特别是涉及隐含收益率曲线斜率的因素;（B）以提高MCMC输出效率的方式对参数进行后验模拟，例如，通过对因因素而被边缘化的参数进行抽样，并对大都会的建议密度进行调整-Hastings步骤使用关于基于模拟退火算法的输出的当前目标的模式和曲率的信息;以及（c）通过重新参数化和平方根滤波递归来减轻拟合中的数值不稳定性的措施。我们应用这些技术来解释1986年1月至2005年12月期间9种美国国库券（期限从1个月到120个月不等）的月收益率。该模型包含三个因素，一个潜在的和两个观察。我们还考虑了预测2006年每个月的9个收益率的问题。我们表明，（多步前进）预测区域正确地括号中的实际产量在这些月份，从而突出了拟合模型的实用价值。
In finance and economics much work has been done on the theoretical modeling and statistical estimation of the yield curve, defined as the relationship between (−1/τ) log pt(τ) and τ, where pt(τ) is the time t price of a zero-coupon bond with payoff 1 at maturity date t+τ. Of considerable current interest are models of the yield curve in which a collection of observed and latent factors determine the market price of factor risks, the stochastic discount factor, and the arbitrage-free bond prices. The model is particularly interesting from a statistical perspective, because the yields are complicated nonlinear functions of the underlying parameters (e.g., those appearing in the evolution dynamics of the factors and those appearing in the model of the factor risks). This nonlinearity tends to produce a likelihood function that is multimodal. In this article we revisit the question of how such models should be fit from the Bayesian viewpoint. Key aspects of the inferential framework include (a) a prior on the parameters of the model that is motivated by economic considerations, in particular, those involving the slope of the implied yield curve; (b) posterior simulation of the parameters in ways to improve the efficiency of the MCMC output, for example, through sampling of the parameters marginalized over the factors and tailoring of the proposal densities in the Metropolis–Hastings steps using information about the mode and curvature of the current target based on the output of a simulating annealing algorithm; and (c) measures to mitigate numerical instabilities in the fitting through reparameterizations and square root filtering recursions. We apply the techniques to explain the monthly yields on nine U.S. Treasury Bills (with maturities ranging from 1 month to 120 months) over the period January 1986–December 2005. The model contains three factors, one latent and two observed. We also consider the problem of predicting the nine yields for each month of 2006. We show that the (multi-step-ahead) prediction regions properly bracket the actual yields in those months, thus highlighting the practical value of the fitted model.