On Arbitrage-Free Pricing of Interest Rate Contingent Claims

Unlike most interest rate claim models, the Ho-Lee model utilizes full information on the current term structure. Unfortunately, the model has a major deficiency in that negative interest rates can occur. This article modifies the model such that interest rates are well behaved.     

Pricing Contingent Claims under Interest Rate and Asset Price Risk

This paper presents a general framework for pricing contingent claims under interest rate and asset price uncertainty. The framework extends Ho and Lee's (1986) valuation framework by allowing not only future interest rates but also future asset prices to depend on the current term structure of interest rates. The approach is shown to provide risk-neutral valuation relationships that are consistent with the initial term structure of interest rates and can be applied to valuation of a broad class of assets including stock options, convertible bonds, and junk bonds.     

A Unified Approach for Pricing Contingent Claims on Multiple Term Structures

This paper provides a unified approach for pricing contingent claims on multiple term structures using a foreign currency analogy. All existing option pricing applications are seen to be special cases of this unified approach. This approach is used to price options on financial securities subject to credit risk.     

Pricing and Hedging of Contingent Claims in Term Structure Models with Exogenous Issuing of New Bonds

If calibrated to an observed term structure of interest rates that only covers a finite range of times-to-maturity an HJM-model of the term structure of interest rates will eventually die out in finite time as bonds reach maturity. This poses problems for the pricing and hedging of certain contingent claims. Therefore, we extend the HJM-model in such a way that it lives on an arbitrary time horizon and possesses term structures that cover a constant finite interval of times-to-maturity. We consider the pricing and hedging of contingent claims in this framework.     

Lattice Models for Pricing American Interest Rate Claims

This article establishes efficient lattice algorithms for pricing American interest-sensitive claims in the Heath, Jarrow, and Morton paradigm, under the assumption that the volatility structure of forward rates is restricted to a class that permits a Markovian representation of the term structure. The class of volatilities that permits this representation is quite large and imposes no severe restrictions on the structure for the spot rate volatility. The algorithm exploits the Markovian property of the term structure and permits the efficient computation of all types of interest rate claims. Specific examples are provided.     

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。     

Pricing Contingent Claims on a Risky Asset and Stochastic Interest Rates: A New Discrete Time Approach

This paper presents a new discrete time approach to pricing contingent claims on a risky asset and stochastic interest rates. The term structure of interest rates is modeled so that arbitrage-free bond prices depend on an observable initial forward rate curve rather than an exogenously specified market price of risk. A restricted binomial process is employed to model both interest rates and an asset price. As a result, a complete market valuation formula obtains. By choosing the parameters of the discrete joint distribution such that, in the limit, the discrete model converges to the continuous one, a model is obtained that requires the estimation of only three parameters. The approach is parsimonious with respect to alternative models in the literature and can be used to price contingent claims on any two state variables. The procedure is used to numerically analyze the effects of the volatility of interest rates on the determination of mortgage contract rates.     

Stochastic Convenience Yield and the Pricing of Oil Contingent Claims

This paper develops and empirically tests a two-factor model for pricing financial and real assets contingent on the price of oil. The factors are the spot price of oil and the instantaneous convenience yield. The parameters of the model are estimated using weekly oil futures contract prices from January 1984 to November 1988, and the model's performance is assessed out of sample by valuing futures contracts over the period November 1988 to May 1989. Finally, the model is applied to determine the present values of one barrel of oil deliverable in one to ten years time.     

An Asymptotic Expansion Approach to Pricing Financial Contingent Claims

We propose a new methodology for the valuation problem of financial contingent claims when the underlying asset prices follow a general class of continuous Itô processes. Our method can be applicable to a wide range of valuation problems including contingent claims associated with stocks, foreign exchange rates, the term structure of interest rates, and even their combinations. We illustrate our method by discussing the Black-Scholes economy when the underlying asset prices follow the continuous diffusion processes, which are not necessarily time-homogeneous. The standard Black-Scholes model on stocks and the Cox-Ingersoll-Ross model on the spot interest rate are simple examples. Then we shall give a series of examples on the valuation formulae including plain vanilla options, average options, and other contingent claims. We shall also give some numerical evidence of the accuracy of the approximations we have obtained for practical purposes. Our approach can be rigorously justified by an infinite dimensional mathematics, the Malliavin-Watanabe-Yoshida theory recently developed in stochastic analysis.     

仿射利率期限结构模型与中国宏观经济预期

本文在仿射模型中推导出预期宏观经济变化和利率期限结构的仿射关系,并在三因子模型中进行实证检验。实证结果显示,无套利利率期限结构模型好于简单的利差方法,能够显著提高对宏观经济的预测能力。三因子模型对近期消费和通货膨胀的变化具有更高的解释能力,对投资、产出和出口的解释能力长期有效。     

New No-arbitrage Conditions and the Term Structure of Interest Rate Futures

Interest rate futures are basic securities and at the same time highly liquid traded objects. Despite this observation, most models of the term structure of interest rate assume forward rates as primary elements. The processes of futures prices are therefore endogenously determined in these models. In addition, in these models hedging strategies are based on forward and/or spot contracts and only to a limited extent on futures contracts. Inspired by the market model approach of forward rates by Miltersen, Sandmann, and Sondermann (J Finance 52(1); 409–430, 1997), the starting point of this paper is a model of futures prices. Using, as the input to the model, the prices of futures on interest related assets new no-arbitrage restrictions on the volatility structure are derived. Moreover, these restrictions turn out to prevent an application of a market model based on futures prices.     

On the Information in the Interest Rate Term Structure and Option Prices

We examine whether the information in cap and swaption prices is consistent with realized movements of the interest rate term structure. To extract an option-implied interest rate covariance matrix from cap and swaption prices, we use Libor market models as a modelling framework. We propose a flexible parameterization of the interest rate covariance matrix, which cannot be generated by standard low-factor term structure models. The empirical analysis, based on US data from 1995 to 1999, shows that option prices imply an interest rate covariance matrix that is significantly different from the covariance matrix estimated from interest rate data. If one uses the latter covariance matrix to price caps and swaptions, one significantly underprices these options. We discuss and analyze several explanations for our findings.     

Multi-factor Affine Term Structure Model with Single Regime Shift: Real Term Structure under Zero Interest Rate

In this paper, we extend the one-factor, single regime shift, affine term structure model with time-dependent regime-shift probability to a multi-factor model. We model the nominal interest rate and the expected inflation rate, and estimate the term structure of the real interest rate in the Japanese government bond market using inflation-indexed bond data under zero interest rates. Incorporating the economic structure that the Bank of Japan terminates the zero interest rate when the expected inflation rate gets out of deflationary regime, we estimate the yield curve of the real interest rate for less than 10 years, consistent with the expectation of the market participants in the Japanese government bond market, where inflation-indexed bonds are traded for only around 10 years.     

公债的利率期限结构与成本管理

在理论上公债期限与公债利率是密切相关的,但是,由于流动性偏好理论的假设前提(有效市场假设)与现实不符,致使"公债期限越短、利息成本越低"的观点在实践中不一定成立.研究表明,只有政府在预测未来债券利率走势方面具有比市场更为优势的地位,它才能够通过期限选择降低债务成本.我国目前正满足这一要求,因而通过期限管理降低债务成本是完全可能的.     

Interest Rate Term Structure Estimation with Exponential Splines: A Note

Vasicek and Fong 11 developed exponential spline functions as models of the interest rate term structure and claim such models are superior to polynomial spline models. It is found empirically that i) exponential spline term structure estimates are no more stable than estimates from a polynomial spline model, ii) data transformations implicit in the exponential spline model frequently condition the data so that it is difficult to obtain approximations in which one can place confidence, and iii) the asymptotic properties of the exponential spline model frequently are unrealistic. Estimation with exponential splines is no more convenient than estimation with polynomial splines and gives substantially identical estimates of the interest rate term structure as well.     

Hedging Interest Rate Risk with Futures Portfolios under Term Structure Effects

This study develops and tests a methodology for reducing interest rate risk in a fixed spot portfolio of assets and liabilities with default-free cash flows. A minimum variance hedge is constructed by adding a portfolio of financial futures to the spot portfolio. Theorems are given which establish necessary and sufficient conditions for the existence of unique and zero-variance hedges. The risk reduction characteristics of the methodology are demonstrated by an empirical analysis.     

Pricing Commodity Spread Options with Stochastic Term Structure of Convenience Yields and Interest Rates

The purpose of this research is to provide a valuation formula for commodity spread options. Commodity spread options are options written on the difference of the prices (spread) of two commodities. From the aspect of commodity contingent claims, it is considered that commodity spread options are difficult to evaluate with accuracy because of the existence of the convenience yield. Hence, the model of the convenience yield is the key factor to price commodity spread options. We use the concept of future convenience yields to develop the model that enriches the stochastic behavior of convenience yield. We also introduce Heath-Jarrow-Morton interest rate model to the valuation framework. This general model not only captures the mean reverting feature of the convenience yield, but also allows us to handle a very wide range of shape that the term structure of convenience yield can take. Therefore our model provides various types of models. The numerical analysis presented in this paper provides some unique features of commodity spread options in contrast to normal options. These characteristics have never been addressed in previous studies. Moreover, it suggests that the existing model overprice commodity spread options through neglecting the effect of interest rates.     

利率市场化和寿险定价利率改革互动研究

随着我国利率市场化的深入推进,寿险定价利率市场化呼之欲出。本文从分析部分国家利率市场化和寿险定价利率市场化互动及影响入手,在总结利率市场化和寿险定价利率市场化的互动对寿险市场影响的基础上,分析了2011年以来我国利率市场化启动对我国寿险市场带来的挑战,并从监管、市场机制和保险公司自身等角度提出了应对挑战的建议。     

美国利率体系及其定价基准

美国利率体系 美国的官方利率为联邦基金利率，主要是通过公开市场操作来使该利率在一个狭窄的目标区间内波动，每年10次的联储公开市场委员会会议将选择并公开一个联邦基金利率目标水平。同时，美联储也会根据联邦基金利率调整对商业银行的贴现窗口利率。