Cross‐sectional Restrictions on the Spot and Forward Term Structures of Interest Rates and Panel Unit Root Tests

In this paper we examine the stationarity of all the rates comprising the USD, GBP, DM and JPY spot and forward term structures. Instead of focussing on short maturity interest rates, as most other papers do, we perform a detailed analysis of the whole range of spot and forward interest rates of the 4 main currencies. We investigate the issue of stationarity within the framework of an equilibrium interest rate model such as Vasicek (1977), that defines the cross-sectional and time series properties that interest rates of various maturities must satisfy. We show that within a one-factor interest rate model, such as Vasicek, all interest rates are restricted to exhibit the same mean reverting behaviour. This restriction allows us to apply more powerful panel unit root tests. This methodology increases considerably the number of observations available and as a result the power of the unit root tests. The higher power of these tests allows us to demonstrate that there does exist mean reversion on the spot and forward US interest rates and the forward DM and GBP interest rates.     

Good-Deal Option Price Bounds for a Non-Traded Event with Stochastic Return: A Note

Cochrane and Sa'a-Requejo (2000, Journal of Political Economy) proposed the good-deal price bounds for the European call option on an event that is not a traded asset, but is correlated with a traded asset that can be used as an approximate hedge. One remarkable feature of their model is that the return on an event process explicitly appears in the option price bounds formula, which offered a contrast with the standard option pricing model. We show that the good-deal option price bounds on a non-traded event are obtained as a closed-form formula, when the return on an event is governed by a mean reverting process.     

A New Spin on the Jumbo/Conforming Loan Rate Differential

This article uses house-price transaction data to estimate volatility in house prices. The volatility parameter is an input into a mortgage-pricing model that is used to simulate the contract interest rate that balances the mortgage contract. By segmenting the house-price transaction into high- and low-valued homes, we are able to estimate a theoretical jumbo/conforming loan rate differential. Simulation results demonstrate that the differences in volatility between high- and low-priced homes can produce a contract loan rate differential, holding all else constant. The article also presents a discussion of the problems inherent to estimating volatilities form assets with infrequent trades and long holding periods.     

A Note on Gaussian Estimation of the CKLS and CIR Models with Feedback Effects for Japan

In this note we extend the Gaussian estimation of two factor CKLS and CIR models recently considered in Nowman, K. B. (2001, Gaussian estimation and forecasting of multi-factor term structure models with an application to Japan and the United Kingdom, Asia Pacif. Financ. Markets 8, 23–34) to include feedback effects in the conditional mean as was originally formulated in general continuous time models by Bergstrom, A. R. (1966, Non-recursive models as discrete approximations to systems of stochastic differential equations, Econometrica 34, 173–182) with constant volatility. We use the exact discrete model of Bergstrom, A. R. (1966, Non-recursive models as discrete approximations to systems of stochastic differential equations, Econometrica 34, 173–182) to estimate the parameters which was first used by Brennan, M. J. and Schwartz, E. S. (1979, A continuous time approach to the pricing of bonds, J. Bank. Financ. 3, 133–155) to estimate their two factor interest model but incorporating the assumption of Nowman, K. B. (1997, Gaussian estimation of single-factor continuous time models of the term structure of interest rates, J. Financ. 52, 1695–1706; 2001, Gaussian estimation and forecasting of multi-factor term structure models with an application to Japan and the United Kingdom, Asia Pacif. Financ. Markets 8, 23–34). An application to monthly Japanese Euro currency rates indicates some evidence of feedback from the 1-year rate to the 1-month rate in both the CKLS and CIR models. We also find a low level-volatility effect supporting Nowman, K. B. (2001, Gaussian estimation and forecasting of multi-factor term structure models with an application to Japan and the United Kingdom, Asia Pacif. Financ. Markets 8, 23–34).     

Continuous-time term structure models: Forward measure approach

The problem of term structure of interest rates modelling is considered in a continuous-time framework. The emphasis is on the bond prices, forward bond prices and so-called LIBOR rates, rather than on the instantaneous continuously compounded rates as in most traditional models. Forward and spot probability measures are introduced in this general set-up. Two conditions of no-arbitrage between bonds and cash are examined. A process of savings account implied by an arbitrage-free family of bond prices is identified by means of a multiplicative decomposition of semimartingales. The uniqueness of an implied savings account is established under fairly general conditions. The notion of a family of forward processes is introduced, and the existence of an associated arbitrage-free family of bond prices is examined. A straightforward construction of a lognormal model of forward LIBOR rates, based on the backward induction, is presented.     

Modelling the Currency Forward Risk Premium: A New Perspective

In this paper we seek to develop a new approach to the time series analysis of foreign exchange risk premia. We do so by assuming a geometric Brownian process for the spot exchange rate and expressing the no-arbitrage spot-forward price relationship under the historical probability measure. We are thereby able to obtain a stochastic differential equation system linking the spot exchange rate, the forward exchange rate and the risk premium (modelled directly as a mean-reverting diffusion process) which we estimate using Kalman filtering techniques. We are able to use observations at a range of frequencies since the framework we set up does not involve overlapping observations. The model is then applied to the French Franc/USD, DEM/USD, GBP/USD, and Japanese Yen/USD exchange rates from 1 January 1990 to 31 December 1998. For all currencies we find evidence that the forward risk premium is stationary and exhibits substantial positive time variation.     

Convex Structure of the Constrained Least Square Problem for Estimating the Forward Rate Sequence

We will show that the constrained least square problem proposed inKonno and Takase [5] for estimating the forward rate sequence by usingthe market prices of default-free non-callable coupon bonds is in facta convex minimization problem under more general conditions than thoseassumed in the subsequent paper by the same authors [6]. Consequently,the constrained least square approach can generate a smooth andaccurate forward rate sequence very fast by standard convexminimization algorithms.     

Finite Dimensional Affine Realisations of HJM Models in Terms of Forward Rates and Yields

Finite dimensional Markovian HJM term structure models provide ideal settings for the study of term structure dynamics and interest rate derivatives where the flexibility of the HJM framework and the tractability of Markovian models coexist. Consequently, these models became the focus of a series of papers including Carverhill (1994), Ritchken and Sankarasubramanian (1995), Bhar and Chiarella (1997), Inui and Kijima (1998), de Jong and Santa-Clara (1999), Björk and Svensson (2001) and Chiarella and Kwon (2001a). However, these models usually required the introduction of a large number of state variables which, at first sight, did not appear to have clear links to the market observed quantities, and the explicit realisations of the forward rate curve in terms of the state variables were unclear. In this paper, it is shown that the forward rate curves for these models are affine functions of the state variables, and conversely that the state variables in these models can be expressed as affine functions of a finite number of forward rates or yields. This property is useful, for example, in the estimation of model parameters. The paper also provides explicit formulae for the bond prices in terms of the state variables that generalise the formulae given in Inui and Kijima (1998), and applies the framework to obtain affine representations for a number of popular interest rate models.     

A Complete Markovian Stochastic Volatility Model in the HJM Framework

This paper considers a stochastic volatility version of the Heath, Jarrow and and Morton (1992) term structure model. Market completeness is obtained by adapting the Hobson and Rogers (1998) complete stochastic volatility stock market model to the interest rate setting. Numerical simulation for a special case is used to compare the stochastic volatility model against the traditional Vasicek (1977) model.     

A Simple Measure for Examining the Proxy Problem of the Short-Rate

The behavior of a finite-maturity yield used as a proxy for the short-rate can deviate substantially from that of the short-rate, which causes estimation biases of model parameters and pricing errors of interest-rate claims. This study proposes a simple measure that visualizes this deviation based on an analytical approximation of the term structure of interest rates. The computation of the measure is almost as easy as that of an affine model, so the adequacy of proxy can be readily checked even for short-rate models that do not admit closed-forms of bond prices.     

流动性、物价稳定与资产价格上涨——从理论模型看日本的经验教训

本文以20世纪80年代中后期的日本为对象，从理论和实证两方面研究在低利率、物价稳定的背景下，资产泡沫形成的原因，以及日本银行货币政策失误的教训，并对我国当前低利率、物价稳定、资产价格上涨并存的现象提出政策建议。本文认为，应避免汇率升值对利率产生过大的影响，维持国内利率政策的独立性；货币政策以物价稳定为主要目标，但应密切关注持续的资产价格上涨；维持稳健的货币政策，防止货币政策矫枉过正。     

关于Riemann可积性的注记

本文用测度论讨论了一元非连续函数的可积性,给出了一元非连续函数Riemann可积的充分条件.     

One Approach to Dual Randomness in Life Insurance

Abstract

1. The Unnatural Hypothesis of a Constant Rate of Interest

There are loan contracts which assume a constant interest during several years and thereafter payment of the amount borrowed, but nowadays clauses are as a rule admitted giving the debtor right of conversion or repayment after a certain period, generally ten years. Low interest loans can be considered as perpetuities from a practical point of view, as long as no possibility is meant to exist that the market rate will fall under their nominal rate. Such a loan—as e.g. Consols—with the nominal rate i ₀ ought to be valued at a discount if the market rate is higher, say i > i ₀, the value being equal to the fraction i ₀ : i. But constant rates are no rule in practice.     

American option valuation under stochastic interest rates

By applying Ho, Stapleton and Subrahmanyam's (1997, hereafter HSS) generalised Geske–Johnson (1984, hereafter GJ) method, this paper provides analytic solutions for the valuation and hedging of American options in a stochastic interest rate economy. The proposed method simplifies HSS's three-dimensional solution to a one-dimensional solution. The simulations verify that the proposed method is more efficient and accurate than the HSS (1997) method. We illustrate how the price, the delta, and the rho of an American option vary between the stochastic and non-stochastic interest rate models. The magnitude of this effect depends on the moneyness of the option, interest rates, volatilities of the underlying asset price and the bond price, as well as the correlation between them. This revised version was published online in June 2006 with corrections to the Cover Date.     

利率与股价之间的价格溢出效应与波动溢出效应

基于具有外生变量的二元VAR-MGARCH模型对中国货币市场利率和股价之间的关联进行了理论分析和实证研究。结果表明,利率和股价之间基本不存在价格溢出效应;货币市场利率和股价序列均表现出时变方差的特征和波动的持久性特征,货币市场和股市之间存在双向波动溢出效应;货币供给的正向冲击对利率的影响是正向的。     

Central Bank Policy Paths and Market Forward Rates: A Simple Model

Increasingly many central banks announce likely paths for future policy rates. Recent experience suggests that market forward rates can differ substantially from those announced. Models commonly adopted in policy analysis ignore such differences. This paper studies a simple model that can capture deviations between announced paths and market forward rates. We detail the macroeconomic transmission of such deviations and show how the model can inform policy deliberations.