Classes of Interest Rate Models under the HJM Framework

Although the HJM term structure model is widely accepted as the mostgeneral, and perhaps the most consistent, framework under which to studyinterest rate derivatives, the earlier models of Vasicek,Cox–Ingersoll–Ross, Hull–White, andBlack–Karasinski remain popular among both academics andpractitioners. It is often stated that these models are special cases ofthe HJM framework, but the precise links have not been fully establishedin the literature. By beginning with certain forward rate volatilityprocesses, it is possible to obtain classes of interest models under theHJM framework that closely resemble the traditional models listed above.Further, greater insight into the dynamics of the interest rate processemerges as a result of natural links being established between the modelparameters and market observed variables.     

On the Quasi Gaussian Interest Rate Models

In this paper some remarks on the interest rate model proposed by Jamishidian (1991) and Ritchken and Sankarasubramanian (1995b) are presented. This revised version was published online in August 2006 with corrections to the Cover Date.     

Modeling the U.S. Short-Term Interest Rate by Mixture Autoregressive Processes

A new kind of mixture autoregressive model with GARCH errorsis introduced and applied to the U.S. short-term interest rate.According to the diagnostic tests developed in the article andfurther informal checks, the model is capable of capturing bothof the typical characteristics of the short-term interest rate:volatility persistence and the dependence of volatility on thelevel of the interest rate. The model also allows for regimeswitches whose presence has been a third central result emergingfrom the recent empirical literature on the U.S. short-terminterest rate. Realizations generated from the estimated modelseem stable and their properties resemble those of the observedseries closely. The drift and diffusion functions implied bythe new model are in accordance with the results in much ofthe literature on continuous-time diffusion models for the short-terminterest rate, and the term structure implications agree withhistorically observed patterns.     

Libor Market Models versus Swap Market Models for Pricing Interest Rate Derivatives: An Empirical Analysis

We empirically compare Libor and Swap Market Models for the pricing of interest rate derivatives, using panel data on prices of US caplets and swaptions. A Libor Market Model can directly be calibrated to observed prices of caplets, whereas a Swap Market Model is calibrated to a certain set of swaption prices. For both models we analyze how well they price caplets and swaptions that were not used for calibration. We show that the Libor Market Model in general leads to better prediction of derivative prices that were not used for calibration than the Swap Market Model. Also, we find that Market Models with a declining volatility function give much better pricing results than a specification with a constant volatility function. Finally, we find that models that are chosen to exactly match certain derivative prices are overfitted; more parsimonious models lead to better predictions for derivative prices that were not used for calibration.     

Libor Market Models versus Swap Market Models for Pricing Interest Rate Derivatives: An Empirical Analysis

We empirically compare Libor and Swap Market Models for thepricing of interest rate derivatives, using panel data on pricesof US caplets and swaptions. A Libor Market Model can directlybe calibrated to observed prices of caplets, whereas a SwapMarket Model is calibrated to a certain set of swaption prices.For both models we analyze how well they price caplets and swaptionsthat were not used for calibration. We show that the Libor MarketModel in general leads to better prediction of derivative pricesthat were not used for calibration than the Swap Market Model.Also, we find that Market Models with a declining volatilityfunction give much better pricing results than a specificationwith a constant volatility function. Finally, we find that modelsthat arechosen to exactly match certain derivative prices areoverfitted; more parsimonious models lead to better predictionsfor derivative prices that were not used for calibration. JELClassification: G12, G13, E43.     

Interest Rates and Exchange Rate Movements: Analyzing Short-term Investments in Long-term Bonds

Tests of the uncovered interest rate parity (UIP) are subject to various data problems when long-term interest rates are applied: due to the long investment period, time intervals for measuring exchange rate movements are usually overlapping and therefore not independent. This shortfall can be prevented by considering short-term investments in long-term bonds instead of investments to maturity. This article analyzes the explanatory power of long-term interest rates with regard to 1- and 3-month exchange rate movements by relating return differences from 1- and 3-month investments in domestic and foreign 10-year government bonds to nine different exchange rates. From a Swiss perspective, there is only weak support for an interrelation between return differences and the corresponding exchange rate movements, whereas from a US perspective, the resulting estimates are much more in line with UIP.The reader may for instance consider Engel (1996) and Froot and Thaler (1990).     

当前金融市场环境下我国商业银行利率风险的防范

传统的存贷款政策、落后的金融市场、利息损益调整的被动局面以及在国际金融业务中风险意识淡薄等原因，严重影响我国商业银行的经营效益，同时也带来巨大的经营风险。建议结合我国商业银行的实际情况及利率市场化的进程，分不同阶段确定不同的重点，循序渐进地进行利率风险管理。     

The Responses of Interest Rate Spreads to Information Releases

This study examines the responses of three popular futures interest-rate spreads--the MOB (Municipals over Treasury bonds), the NOB (Notes over Treasury bonds), and the TED (Treasury Bills over Eurodollars) to macroeconomic news. We find responses to differ across the three spreads. The most pronounced responses are displayed by the MOB, followed by the NOB and the TED. We also find that the spreads take time to adjust to news in the announcements.     

The Interest Rate Exposure of Nonfinancial Corporations

Many interest rates are as volatile as exchange rates and thus represent an equallyimportant source of risk for corporations. While this is true not only for financialinstitutions, but for other corporations as well, little is known about the interest rateexposure of nonfinancial firms. Consequently, this paper investigates the impact ofinterest rate risk on a large sample of nonfinancial corporations. It presents empiricalevidence for the existence of linear and nonlinear exposures with regard to movementsin various interest rate variables. The interest rate exposure is empirically determinedby measures of firm liquidity, but not by financial leverage.     

On the Nonlinear Specifications of Short-Term Interest Rate Behavior: Evidence from Euro-Currency Markets

This paper presents a coherent nonlinear interest rate model that incorporates the dynamics of the error correction specification into the traditional term structure model. The joint tests based on six Euro-Currency rates indicate that the linear specification should be rejected. The estimated equation suggests that the linear components—the change of the long-term interest rate and the error correcting term are highly significant. The nonlinear components involving the higher order of the independent variables, the cross products, the lagged error squares, and/or the ARCH effect also present significant explanatory power for predicting short-term Euro-Currency rate changes, confirming the non-linear specifications.     

Sources of Bank Interest Rate Risk

We investigate bank stocks'sensitivity to changes in interest rates and the factors affecting this sensitivity. We focus on whether the exposure of commercial banks to interest rate risk is conditioned on certain balance sheet and income statement ratios. We find a significantly negative relation between bank stock returns and changes in interest rates over the period 1991–1996. We also find that bank characteristics measured from basic financial statement information explain bank stocks'sensitivity to interest rate changes. These results suggest that bank managers, analysts, and regulators can use this information to assess the relative risk exposure of banks.     

On Forest Rotation under Interest Rate Variability

The current literature on optimal forest rotation makes the unrealistic assumption of a constant interest rate although harvesting decisions of forest stands are typically subject to relatively long time horizons. We apply the single rotation framework to extend the existing studies to cover the unexplored case of variable interest rate. We show that even in the deterministic case if the current interest rate deviates from its long-run steady state, interest rate variability may change the rotation age significantly when compared with the constant discounting case. Further, and importantly, allowing for interest rate uncertainty as a mean reverting process and forest value as a geometric Brownian motion, we can provide an explicit solution for the two dimensional path-dependent optimal stopping problem. Increased interest rate volatility is shown to lengthen the optimal rotation period. Numerical calculations show that interest rate volatility has a large quantitative importance.     

Optimal Insurance Design Under a Value-at-Risk Framework

This study designs an optimal insurance policy form endogenously, assuming the objective of the insured is to maximize expected final wealth under the Value-at-Risk (VaR) constraint. The optimal insurance policy can be replicated using three options, including a long call option with a small strike price, a short call option with a large strike price, and a short cash-or-nothing call option. Additionally, this study also calculates the optimal insurance levels for these models when we restrict the indemnity to be one of three common forms: a deductible policy, an upper-limit policy, or a policy with proportional coinsurance. JEL Classification No: G22     

低利率环境下的政府债务成本与财政政策选择

在未来较长时间内,名义利率和实际利率可能保持低位,低利率压缩了货币政策操作空间,较低的财政成本和较高财政收入,意味着财政政策应该且能够更多发挥更大作用。在政府债务稳定与产出稳定的权衡中,应更多关注产出稳定。     

REIT Risk Premium Sensitivity and Interest Rates

This analysis investigates several aspects of the relationship between daily REIT stock risk premiums and various interest rates. Consistent with prior research, the general findings indicate that interest rates do impact REIT returns. This study specifically finds that stock returns are more sensitive to maturity rate spread between short- and long-term treasuries than the credit rate spread between commercial bonds and treasuries. In addition, the analyses document a structural model shift during the nineties that has made REITs more sensitive to credit risk. In additional to change in investor clientele, an analysis of declining REIT credit-worthiness points to a root cause for this shift.     

Junp-Diffusion Interest Rate Process: An Empirical Examination

We investigate a jump-diffusion process, which is a mixture of an O-U process used by Vasicek (1977) and a compound Poisson jump process, for the term structure of interest rates. We develop a methodology for estimating the jump-diffusion model and complete an empirical study in comparing the model with the Vasicek model, for the US money market interest rates. The results show that when the short-term interest rate is low, both models predict an upward sloping term structure, with the jump-diffusion model fitting the actual term structure quite well and the Vasicek model overestimating significantly. When the short-term interest rate is high, both models predict a downward sloping term structure, with the jump-diffusion model underestimating the actual term structure more significantly than the Vasicek model.     

利率掉期交易在我国现阶段的作用探讨

何为利率掉期？在目前我国的商业银行中，利率掉期的开展将会起到怎么样的积极作用？又将会面临怎么样的问题呢？本文将试图从这些方面做一定的阐述和探讨。     

Production and the Real Rate of Interest: A Sample Path Equilibrium

This paper examines a multiperiod production economy where investorsdo not observe the realizations of productivity factors or securityexpected returns. Unlike previous work, which expresses theequilibrium conditions as functions of unobservable (to bothreal-world investorsand empiricists) moments of the distributionsof returns, we express the equilibrium real rate asa functionof the observable sample paths of realizations of returns. Weprovide a framework for empirically testing this and other assetpricing models without outside-the-model econometric assumptionsneeded for producing the unobservable moments of returns. Weconstruct versions of the restrictions for any time intervalbetween observations. JEL codes: E43, G12, D92, D80, D51     

A Two-Factor Model for Low Interest Rate Regimes

This paper derives a two-factor model for the term structure of interest rates that segments the yield curve in a natural way. The first factor involves modelling a non-negative short rate process that primarily determines the early part of the yield curve and is obtained as a truncated Gaussian short rate. The second factor mainly influences the later part of the yield curve via the market index. The market index proxies the growth optimal portfolio (GOP) and is modelled as a squared Bessel process of dimension four. Although this setup can be applied to any interest rate environment, this study focuses on the difficult but important case where the short rate stays close to zero for a prolonged period of time. For the proposed model, an equivalent risk neutral martingale measure is neither possible nor required. Hence we use the benchmark approach where the GOP is chosen as numeraire. Fair derivative prices are then calculated via conditional expectations under the real world probability measure. Using this methodology we derive pricing functions for zero coupon bonds and options on zero coupon bonds. The proposed model naturally generates yield curve shapes commonly observed in the market. More importantly, the model replicates the key features of the interest rate cap market for economies with low interest rate regimes. In particular, the implied volatility term structure displays a consistent downward slope from extremely high levels of volatility together with a distinct negative skew. 1991 Mathematics Subject Classification: primary 90A12; secondary 60G30; 62P20 JEL Classification: G10, G13