A Simple Induction Approach and an Efficient Trinomial Lattice for Multi-State Variable Interest Rate Derivatives Models

This paper presents an alternative approach for interest rate lattice construction in the Ritchken and Sankarasubramanian (1995) framework. The proposed method applies a parsimonious induction technique to represent the distribution of auxiliary state variables and value interest rate derivatives. In contrast to other approaches, this technique requires no numerical interpolations, approximations and iterative procedures for pricing interest rate options using a simple backward induction and, therefore, provides significant computational advantages and flexibility with respect to existing implementations. Also, the proposed trinomial interest rate lattice specification provides for a further reduction in computational costs with additional flexibility. The results of this work can be extended to a class of derivatives pricing models with path dependent state variables and generalized to multi-factor models.     

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.     

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.     

The GARCH Option Pricing Model: A Modification of Lattice Approach

Ritchken and Trevor (1999) proposed a lattice approach for pricing American options under discrete time-varying volatility GARCH frameworks. Even though the lattice approach worked well for the pricing of the GARCH options, it was inappropriate when the option price was computed on the lattice using standard backward recursive procedures, even if the concepts of Cakici and Topyan (2000) were incorporated. This paper shows how to correct the deficiency and that with our adjustment, the lattice method performs properly for option pricing under the GARCH process. JEL Classification: C10, C32, C51, F37, G12     

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.     

Models with Unexpected Components: The Case for Efficient Estimation

Financial models often use unexpected explanatory variables. Conventionally, these are generated as the residuals of auxiliary equations, which are then substituted into the model of interest in a second step. This induces an econometric problem into the estimates, which is typically ignored. We propose a maximum likelihood estimation method as a solution. While there may be a predisposition when using financial data to dismiss our method as difficult to specify correctly, Monte Carlo simulations show that our method is robust. Further, we show that the magnitude of errors due to the generated regressor problem is somewhat larger than that due to ignoring the effects of plausible levels of leptokurtosis. An empirical example using commercial bank stock returns finds that hypothesis test conclusions from the conventional method can often be overturned.     

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.     

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.     

基于GARCH类模型的人民币汇率非线性依赖关系研究

利用三类不同结构的基本 GARCH 类模型对四个不同时间跨度上人民币汇率序列进行拟合和效度检验;并进一步结合窗口检验程序,借助相关性 C 统计量和双相关 H 统计量对实证对象的 GARCH 类非线性结构的稳定性及 GARCH 类模型中有关非线性相关的基本假设进行检验。结果表明,人民币汇率系统是一个典型的非线性动态复杂系统,人民币汇率序列中的 GARCH 类非线性结构表现出了非持续和瞬时性的特点。     

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.     

Calibration of Gaussian heath, Jarrow and Morton and random field interest rate term structure models

We show how the recently introduced Gaussian random field interest rate term structure models can be calibrated accurately and quickly to market caps and swaptions prices. We show how the calibrated random field model can be approximated arbitrarily closely with a multi-factor Gaussian Heath, Jarrow and Morton model. We argue that the Gaussian random field model is easier to calibrate and can be used as an indirect way to calibrate multi-factor Gaussian Heath, Jarrow and Morton interest rate models.This work was carried out when the author was at the Financial Options Research Centre, Warwick Business School, University of Warwick. I wish to thank Stewart Hodges for many helpful discussions and comments and Martin Cooper of Tokai Bank, Europe, for supplying the data used in this paper. I also wish to thank the Economic and Social Research Council and FORC for funding. An earlier version of this paper entitled Multi-Factor Gaussian HJM Approximation to Kennedy and Calibration to Caps and Swaptions Prices was presented at the 9th Annual Conference, FORC., Warwick Business School, September 1996. Another version also appears in the author's Ph.D. thesis. I am grateful to the helpful comments provided by Marti Subrahmanyam and the two anonymous referees. All errors are my own and the views expressed in no way reflect the opinion of my employer.     

The Valuation of Interest Rate Digital Options and Range Notes Revisited

The aim of this paper is to value interest rate structured products in a simpler and more intuitive way than Turnbull (1995). Considering some assumptions with respect to the evolution of the term structure of interest rates, the price of a European interest rate digital call option is given. Recall it is a contract designed to pay one dollar at maturity if a reference interest rate is above a prespecified level (the strike), and zero in all the others cases. Combining two options of this type enables us to value a European range digital option. Then using a one factor linear gaussian model and the new well‐known change of numeraire approach, a closed‐form formula is found to value range notes which pay at the end of each defined period, a sum equal to a prespecified interest rate times the number of days the reference interest rate lies inside a corridor.     

The Equilibrium Exchange Rate of Mauritius: Evidence from Two Structural Models

In this paper we assess the equilibrium value of the Mauritian rupee in 2006-7 and over the medium run using two structural models. First, we derive a current account-based measure of the exchange rate equilibrium using the macroeconomic balance approach. Second, we estimate a reduced-form fundamental equilibrium exchange rate measure. Our results, which are robust to an alternative non-econometric approach, suggest that the Mauritian rupee was aligned with its equilibrium value in 2006-7 and little adjustment appeared necessary over the medium run.     

Hysteresis Models of Investment with Multiple Uncertainties and Exchange Rate Risk

In this article we use the hysteresis model of investment developed by Brennan and Schwartz, and Dixit, and we extend it to capture the impact of interacting uncertainties on a firm with foreign operations. We develop a three-country, four-factor model where both continuous revenues and continuous costs are stochastic and are generated in countries other than the home country of the investor, who has to carry foreign currencies' risk. All four state-variables follow geometric Brownian motion processes. A critical assumption is made that the capital outlays for switching between the idle and the active states are constant fractions of the costs. An efficient numerical solution is used to demonstrate applications of the model on a multinational corporation facing operating and exchange rate risks in a multistage investment setting with interacting investment and operating options.     

我国银行间同业拆放利率影响因素的实证分析

银行间同业拆放市场利率是我国主要的货币市场利率,也是最早实现市场化的利率.对商业银行来说,同业拆放利率是商业银行决定贷款利率与存款利率的重要标准.本文通过建立单整自回归平均移动模型ARIMA,研究一年期人民币银行贷款利率、一年期人民币储蓄存款利率、三年期凭证式国债利率、法定准备金年利率、回购利率、消费价格指数、综合股价指数、金融机构各项贷款与存款总额比值和人民币对美元汇率这些因素对我国银行间拆放利率的影响.研究结果表明:一年期人民币银行贷款利率和回购利率是影响我国银行间同业拆放利率的主要因素.