Arbitrage-free valuation of interest rate securities under forward curves with stochastic speed and acceleration

Arbitrage-free models for valuing interest rate securities posit that stochastic changes in spot or forward interest rates (forward rate “speed”) follow a diffusion process. This paper extends the Heath, Jarrow and Morton [Bond pricing and the term structure of interest rates: a new methodology for contingent claims valuations, Econometrica 60 (1992) 77-105], HJM framework by allowing diffusive shocks to both the “speed” and “acceleration” of forward rates. The arbitrage-free restriction on forward rates is identified and involves volatilities of the speed and acceleration dynamics and their correlation. Although the extended forward rates remain in the diffusive framework and evolve continuously, they may exhibit large changes over short intervals (as with jumps) due to stochastic acceleration. Comparisons of bond prices show that the proposed model generates more complex and intricate shapes for the restricted forward curve with the same number of stochastic factors and volatility.     

Estimating value-at-risk under a Heath–Jarrow–Morton framework with jump

This article proposes a new methodology for measuring Value-at-Risk (hereafter VaR) using a model that incorporates both volatility and jumps. Heath–Jarrow–Morton (HJM) model has been used for the valuation of interest rate derivatives. This study extends the use of HJM model to the estimation VaR. This article specifically uses a two-factor HJM jump-diffusion model for the computation. The study models the Eurodollar futures prices using its derivatives. In addition, this article uses a new volatility specification of Ze-To (2002) to construct the HJM dynamics. The result indicates that the VaR model using HJM jump-diffusion framework performs well in capturing the nonnormality and in providing accurate VaR forecasts in the in-sample and out-sample tests.     

Convergence within the EU: Evidence from Interest Rates

The economic and political changes which are taking place in Europe affect interest rates. This paper develops a two-factor model for the term structure of interest rates specially designed to apply to EMU countries. In addition to the participant country's short-term interest rate, we include as a second factor a 'European' short-term interest rate. We assume that the 'European' rate follows a mean reverting process. The domestic interest rate also follows a mean reverting process, but its convergence is to a stochastic mean which is identified with the 'European' rate. Closed-form solutions for prices of zero coupon discount bonds and options on these bonds are provided. A special feature of the model is that both the domestic and the European interest rate risks are priced. We also discuss an empirical estimation focusing on the Spanish bond market. The 'European' rate is proxied by the ecu's interest rate. Through a comparison of the performance of our convergence model with a Vasicek model for the Spanish bond market, we show that our model provides a better fit both in-sample and out-of sample and that the difference in performance between the models is greater the longer the maturity of the bonds.
(J.E.L.: E43, C510).     

State prices,liquidity, and default

We show, in a monetary exchange economy, that asset prices in a complete markets general equilibrium are a function of the supply of liquidity by the Central Bank, through its effect on default and interest rates. Two agents trade goods and nominal assets to smooth consumption across periods and future states, in the presence of cash-in-advance financing costs that have effects on real allocations. We show that higher spot interest rates reduce trade and as a result increase state prices. Hence, states of nature with higher interest rates are also states of nature with higher risk-neutral probabilities. This result, which cannot be found in a Lucas-type representative agent model, implies that the yield curve is upward sloping in equilibrium, even when short-term interest rates are fairly stable and the variance of the (macroeconomic) stochastic discount factor is 0. The risk-premium in the term structure is, therefore, a monetary-cost risk premium.     

Quantile hedging for equity-linked life insurance contracts in a stochastic interest rate economy

In this paper we examine equity-linked life insurance contracts in a stochastic interest rate economy via quantile hedging whose purpose is to look for the optimal probability of a successful hedge under initial budget constraint. Most of the existing studies have focused on valuing equity-linked life insurance contracts by quantile hedging or in a framework of stochastic interest rates. However, a few have taken into account simultaneously the two techniques, which make valuing equity-linked life insurance contracts more difficult. We model the term structure of interest rates by classical HJM model that imbeds stochastic interest rate economy into one containing an arbitrary number of additional risky assets. By means of the change of measure approach, we give explicit formulas for the fair values of the following four products: deterministic payoff contract, pure equity-linked life contract, equity-linked life contract with guarantee, equity-linked life contract with minimum guarantees and capped benefits. We find that the explicit formulas are mainly composed of normal distribution functions and two-dimensional normal distribution functions. We also investigate sensibility of the survival probability using data of interest rates, stock prices and life table from China.     

Asset allocation under stochastic interest rate with regime switching

We investigate an optimal asset allocation problem in a Markovian regime-switching financial market with stochastic interest rate. The market has three investment opportunities, namely, a bank account, a share and a zero-coupon bond, where stochastic movements of the short rate and the share price are governed by a Markovian regime-switching Vasicek model and a Markovian regime-switching Geometric Brownian motion, respectively. We discuss the optimal asset allocation problem using the dynamic programming approach for stochastic optimal control and derive a regime-switching Hamilton–Jacobi–Bellman (HJB) equation. Particular attention is paid to the exponential utility case. Numerical and sensitivity analysis are provided for this case. The numerical results reveal that regime-switches described by a two-state Markov chain have significant impacts on the optimal investment strategies in the share and the bond. Furthermore, the market prices of risk in both the bond and share markets are crucial factors in determining the optimal investment strategies.     

Monetary equilibria over an infinite horizon

Summary. Money provides liquidity services through a cash-in-advance constraint. The exchange of commodities and assets extends over an infinite horizon under uncertainty and a sequentially complete asset market. Monetary policy sets the path of rates of interest and accommodates the demand for balances through open market operations or loans. A public authority, which, most pertinently, inherits a strictly positive public debt, raises revenue from taxes and seignorage, and it distributes possible budget surpluses to individuals through transfers. Competitive equilibria exist, under mild solvency conditions. But, for a fixed path of rates of interest, there is a non-trivial multiplicity of equilibrium paths of prices of commodities. Determinacy requires that, subject to no-arbitrage and in addition to rates of interest, the prices of state-contingent revenues be somehow determined.Received: 16 April 2003, Revised: 16 January 2004, JEL Classification Numbers: D50, E40, E50.We are grateful to Pietro Reichlin, Rabah Amir, Tomoyuki Nakajima, Armando Dominioni and Leo Ferraris for helpful discussions and their reading of preliminary drafts. The usual disclaimer applies. An earlier version was circulated as [4].     

A nonparametric method for term structure fitting with automatic smoothing

We present a nonparametric method for fitting the term structure of interest rates from bond prices. Our method is a variant of the smoothing spline approach, but within our framework we are able to determine the smoothing coefficient automatically from data using the generalized cross-validation or maximum likelihood estimates. We present an effective numerical algorithm to simultaneously find the term structure and the optimal smoothing coefficient. Finally, we compare the proposed nonparametric fitting method with other parametric and nonparametric methods to find its superior performance. We find that existing term structure fitting methods perform well in liquid markets while illiquid markets present new challenges, which we address in this article.     

Money Demand and Purchasing Power Parity (PPP), in the Republic of South Africa

We have examined empirically two important economic relationships, the Purchasing Power Parity (PPP) and the money demand relationship, among the consumer prices, money, output, interest rates, and the nominal rand/dollar exchange rate of the Republic of South Africa (RSA) for the sample period from 1993 second quarter to 2003 second quarter within the frameworks of co-integration and Error Correction Model (ECM). It is established that the strong version of the PPP including the proportionality and the symmetry hypothesis, is supported. The changes in the rand/dollar exchange rates are influenced by the long term trends in the consumer prices of the RSA and the USA. There also exists a well defined money demand function for this period. The broad money demand is influenced by the consumer prices, the GDP and the interest rates. The short-term interest rates are found to be the own rate of return for broad money and the long-term bond yield is the opportunity cost of holding money. The monetary policy works through the short term interest rates.

     

中国利率期限结构中的宏观经济风险因素分析——基于宏观-金融模型的研究途径

本文应用宏观-金融模型对我国利率期限结构动态过程中的时变宏观经济风险价格进行定量估计,在此基础上,对利率期限结构的预期成分和风险溢价成分进行分解,并且模拟了宏观经济对利率期限结构的冲击效应。研究结果表明,我国利率期限结构中存在着显著的时变宏观经济风险价格;不同期限利率可以明显地分解出预期成分和风险溢价成分,风险溢价成分的变动具有阶段性特点;宏观经济冲击在短期内对利率期限结构的整体水平与坡度均有明显影响,在长期内则仅对整体水平的影响较为明显。因此,我国利率期限结构可以体现出宏观经济形势的变化,应该进一步提高利率期限结构在货币政策制定中的作用。     

基于动态Nelson-Siegel模型的国债管理策略分析

本文研究动态Nelson-Siegel模型在中国国债市场上的定价能力、预测能力和套期保值能力.实证发现动态模型对国债利率的样本内定价效率高,适用于中期债券定价;应用于动态预测未来市场利率,预测效果显著优于其他时间序列模型,超出了传统的无套利均衡模型;采用该模型下的久期向量免疫技术,能为国债组合提供更好的动态套期保值效果.本研究在中国国债组合积极和消极管理策略中具有实用价值.     

Bond risk premia,macroeconomic fundamentals and the exchange rate

We propose a two-country no-arbitrage term-structure model to analyze the joint dynamics of bond yields, macroeconomic variables and the exchange rate. The model allows to understand how exogenous shocks to the exchange rate affect the yield curves, how bond yields co-move in different countries and how the exchange rate is influenced by interest rates, macro-economic variables and time-varying bond risk premia.Estimating the model with US and German data, we find that time-varying bond risk premia account for a significant portion of the variability of the exchange rate: apparently, a currency tends to appreciate when investors expect large capital gains on long-term bonds denominated in that currency. A number of other novel empirical findings emerge.     

No-arbitrage, state prices and trade in thin financial markets

We examine how non-competitiveness in financial markets affects the choice of asset portfolios and the determination of equilibrium prices. In our model, potential arbitrage is conducted by a few highly specialized institutional investors who recognize and estimate the impact of their trades on financial prices. We apply a model of economic equilibrium, based on Weretka (, 2007a), in which price effects are determined endogenously as part of the equilibrium concept. For the case in which markets allow for perfect insurance, we argue that the principle of no-arbitrage asset pricing is consistent with non-competitive behavior of the arbitragers and extend the fundamental theorem of asset pricing to the non-competitive setting.     

Bond risk premia, macroeconomic fundamentals and the exchange rate

We propose a two-country no-arbitrage term-structure model to analyze the joint dynamics of bond yields, macroeconomic variables and the exchange rate. The model allows to understand how exogenous shocks to the exchange rate affect the yield curves, how bond yields co-move in different countries and how the exchange rate is influenced by interest rates, macro-economic variables and time-varying bond risk premia.Estimating the model with US and German data, we find that time-varying bond risk premia account for a significant portion of the variability of the exchange rate: apparently, a currency tends to appreciate when investors expect large capital gains on long-term bonds denominated in that currency. A number of other novel empirical findings emerge.     

Will euro area house prices sharply decrease?

The long-term euro area house price equilibrium and its short-term dynamics are estimated by means of a panel error correction model. The estimates show that the short-term dynamics are essentially driven by the autoregressive term (persistence), disposable income and mortgage loans, whereas interest rates have little effect. The long-term house price equilibrium is mainly driven on the demand side by disposable income, interest rates, and mortgage loans, whereas costs (mostly land) drive the equilibrium on the supply side. The unprecedented long-lasting boom in house prices from 1997 to 2007 is thus essentially explained by a favourable macroeconomic development caused by the EMU effect and a glut of global savings. The bust phase of euro area house prices began in 2007, and the current house price might return to its equilibrium level in 2014. According to the most realistic scenario, euro area house prices will experience a smooth and soft landing in 2016 and then begin an increasing phase that will be pulled upwards by a higher equilibrium price. However, a deflationary scenario cannot be excluded if the current credit squeeze is not solved, particularly in the peripheral euro area member states.     

A Theory of Exchange Rates and the Term Structure of Interest Rates

This paper defines the concepts of indirect and direct risk premium effects and analyzes their properties in an exchange rate model. In the model, these effects are endogenously determined in a rational expectations equilibrium. For the effect of an interest rate shock, they have the opposite signs and the indirect risk premium effect can dominate the direct risk premium effect under reasonable parameters. This means that domestic short‐term bonds and foreign bonds are complements in the model even though domestic long‐term bonds and foreign bonds are substitutes. This model, focusing on the indirect risk premium effect and on the term structure of interest rates, can be combined with a small sample bias approach to explain stylized facts about the forward premium anomaly, which is found for short‐term interest rates, but not for long‐term interest rates.     

基于我国国债的利率期限结构曲线估计

本文通过选取不同的样条函数,对某个特定日期国债所隐含的利率期限结构曲线进行回归估计.我们对回归结果的各分段样条函数进行了检验,根据各分段样条函数的估计结果,提出了指数样条函数与多项式样条函数在估计利率期限结构曲线中的一些特点.我们得到的利率期限结构曲线能够很好的反映市场利率.     

On the comparison of Schwartz and Smith’s two- and three-factor models on commodity prices

Since Schwartz and Smith (2000) published their study on two-factor model on commodity prices, many studies have used this model and others have extended it. The authors also proposed the three-factor model due to the poor fitting of the two-factor one on long-term futures prices. At that time the authors had only long-term prices from a private source to calibrate, test and compare these models. No public data on long-term future contracts were available. On the other hand, during the last decade the commodity prices soared as did the liquidity of long-term contracts. This means that the interest of the agents in the management of their risk on long-term positions increased the same way and this is the motivation for this study. In this article, we revisit the comparison between two- and three-factor models using public data for short- and long-term contracts (we use up to the 67-month-ahead contract). We also provide a detailed derivation of the three-factor model differently from that of the original article. Following the original article of Schwartz and Smith, we used oil futures prices traded on the New York Mercantile Exchange to calibrate the model. The results show a better fit of the three-factor model for the term structure of prices and volatilities mainly for long maturities contracts, while the two-factor model in most portions of the curve underestimates the risk premiums. This type of analysis is important not only for daily agents negotiating the physical commodities through long-term contracts but also for investment decisions on development of real projects.     

Some recent developments in capital market theory: A survey

This paper surveys some recent developments in the theory of capital markets. Particular emphasis is given to two strands of the literature. The first covers some recent and fundamental extensions to the theory of risk aversion and the demand for risky assets. These papers are concerned with the effect of non-hedgeable background risk on risk attitudes. The important implications for finance are for the size of the risk premium (the equity premium puzzle) and for the demand for and pricing of contingent claims. For example, background risk may help to explain the apparent over-pricing of options on equity indices. The second topic is interest rate term structure models. Stochastic term structure models try to capture the possible future shapes of the term structure of interest rates. This is relevant for the pricing of contingent claims, in particular for the pricing of interest rate derivatives such as American-style swaptions. The paper will survey the most important recent models in the literature, each of which satisfies the fundamental no-arbitrage property. It will discuss the implications of the models for the pricing of both European-style and American-style options.