Evolution Of Interest Rates Research Articles

Interest Rates and Company Valuation

Interest rates have a considerable bearing on share prices. Any investor’s experience shows that, in general, when interest rates fall significantly, share prices rise, and vice-versa. We begin by observing the evolution of interest rates in the last 22 years in the United States. We also look at changes in the yield curve.

On the valuation of reverse mortgages with regular tenure payments

For the valuation of reverse mortgages with tenure payments, this article proposes a specific analytic valuation framework with mortality risk, interest rate risk, and housing price risk that helps determine fair premiums when the present value of premiums equals the present value of contingent losses. The analytic valuation of reverse mortgages with tenure payments is more complex than the valuation with a lump sum payment. This study therefore proposes a dimension reduction technique to achieve a closed-form solution for reverse annuity mortgage insurance, conditional on the evolution of interest rates. The technique provides strong accuracy, offering important implications for lenders and insurers.

Subordinated [formula omitted]-stable Ornstein–Uhlenbeck process as a tool for financial data description

The classical financial models are based on the standard Brownian diffusion-type processes. However, in the exhibition of some real market data (like interest or exchange rates) we observe characteristic periods of constant values. Moreover, in the case of financial data, the assumption of normality is often unsatisfied. In such cases the popular Vasiček model, that is a mathematical system describing the evolution of interest rates based on the Ornstein–Uhlenbeck process, seems not to be applicable. Therefore, we propose an alternative approach based on a combination of the popular Ornstein–Uhlenbeck process with a stable distribution and subdiffusion systems that demonstrate such characteristic behavior. The probability density function of the proposed process can be described by a Fokker–Planck type equation and therefore it can be examined as an extension of the basic Ornstein–Uhlenbeck model. In this paper, we propose the parameters’ estimation method and calibrate the subordinated Vasiček model to the interest rate data.

On the valuation of compositions in Lévy term structure models

We derive explicit valuation formulae for an exotic path-dependent interest rate derivative, namely an option on the composition of LIBOR rates. The formulae are based on Fourier transform methods for option pricing. We consider two models for the evolution of interest rates: an HJM-type forward rate model and a LIBOR-type forward price model. Both models are driven by a time-inhomogeneous Lévy process.

Global Asset Allocation in Fixed Income Markets

Many global investors are faced with the problem of choosing an appropriate currency allocation of their assets in the capital markets. This paper addresses the asset allocation problem under the assumption that the investment universe is comprised of unhedged risk-free bonds in different countries. In general, the total return arising from holding an unhedged bond portfolio is comprised of two components. One component of the return arises from the bond price changes resulting from yield curve movements and the other component arises from exchange rate fluctuations. In this paper, bond price changes are assumed to be governed by a one factor interest rate term structure model. The return arising from exchange rate changes is extracted by modelling the evolution of exchange rates as a jump stochastic process. The jump process is assumed to occur in the volatility of exchange rate returns. This model is consistent with the empirical evidence that the volatility of currency returns exhibits GARCH behaviour. Using the models that describe the evolution of interest rates and exchange rates, the optimal portfolio allocation problem is solved in a mean-variance setting by Monte Carlo simulation. The out-of-sample performance of the portfolios selected is also presented and is compared against those obtained using other existing methods.

Extending the universality of the Heath–Jarrow–Morton model

Heath, Jarrow, and Morton (HJM) developed an important model of the evolution of interest rates. A key assumption of the model is that interest rate changes are normally distributed in continuous time. Implementing the HJM-method of evolution of interest rates in discrete time for more complex volatility functions remains a significant challenge. In this article, we present a relatively simple and flexible method of implementation, that extends the usefulness of the HJM model. The derivation assumes that the distribution of interest rates is stable, but not necessarily identical, for each discrete time period. This allows us to identify the drift-adjustment terms necessary to build interest rate lattices and trees and Monte Carlo simulations that satisfy exactly the no-arbitrage and volatility conditions, even complex ones, of the model. The much more difficult discrete-time implementation methods suggested in the literature (Heath, Jarrow, and Morton (1991) [Heath, D., Jarrow, R. & Morton, A. (1991). Contingent claim valuation with a random evolution of interest rates. Review of Futures Markets, 54–76.] and Jarrow (1996) [Jarrow, R. (1996). Modeling fixed income securities and interest rate options. New York, NY: McGraw-Hill Companies Inc.]) do not accomplish that. We illustrate our analytical implementation with three examples of volatility functions and demonstrate its superiority to other methods of implementation.

OPTIMAL STRATEGIES FOR THE ISSUANCES OF PUBLIC DEBT SECURITIES

We describe a model for the optimization of the issuances of Public Debt securities developed together with the Italian Ministry of Economy and Finance. The goal is to determine the composition of the portfolio issued every month which minimizes a specific "cost function". Mathematically speaking, this is a stochastic optimal control problem with strong constraints imposed by national regulations and the Maastricht treaty. The stochastic component of the problem is represented by the evolution of interest rates. At this time the optimizer employs classic Linear Programming techniques. However more sophisticated techniques based on Model Predictive Control strategies are under development.

Management of non-maturing deposits by multistage stochastic programming

The management of non-maturing account positions in a bank’s balance like savings and sight deposits as well as certain types of variable-rate mortgages is complicated by the embedded options that its clients may exercise. In addition to the usual interest rate risk, uncertainty in the timing and amount of cash flows must be taken into account when investment or refinancing strategies are determined. This paper introduces a multistage stochastic programming model where the stochastic evolution of interest rates and volume under management is described by stochastic processes in discrete time. Scenarios are generated by means of barycentric approximation which is particularly useful to deal with the observed correlations between interest rates and volume. Practical experience from the application at a major Swiss bank is reported where the model has been employed since the mid-90s.

Modelling Taylor rule uncertainty: an application to the euro area

This paper presents a methodology to estimate an asymmetric probability density function for a forward-looking version of the Taylor interest rate, assuming that not only the explanatory variables but also the parameters of the rule are random variables. The methodology allows for correlation across different sources of uncertainty and the resulting distribution for the Taylor interest rate is obtained by numerical simulation, avoiding any assumption concerning the aggregation of non-normal distributions. The paper presents an application for the euro area as a whole. The main conclusion is that the uncertainty surrounding the Taylor interest rate could be high, i.e. the confidence intervals could be too wide to give clear indications concerning the evolution of interest rates.

Modelling Taylor rule uncertainty: an application to the euro area

This paper presents a methodology to estimate an asymmetric probability density function for a forward-looking version of the Taylor interest rate, assuming that not only the explanatory variables but also the parameters of the rule are random variables. The methodology allows for correlation across different sources of uncertainty and the resulting distribution for the Taylor interest rate is obtained by numerical simulation, avoiding any assumption concerning the aggregation of non-normal distributions. The paper presents an application for the euro area as a whole. The main conclusion is that the uncertainty surrounding the Taylor interest rate could be high, i.e. the confidence intervals could be too wide to give clear indications concerning the evolution of interest rates.

Bond management and max–min optimal control

An immunization problem is considered in which a bond portfolio is to be periodically rebalanced. Max–min optimal control is applied to the problem. The target is to maximize the final portfolio value under the worst possible evolution of interest rates. The optimal control law, obtained by means of dynamic programming, turns out to be different from any duration-based immunization policy.

Term Structure Estimation - An Implied Norm Approach: Negative Option Prices - A Puzzle or Just Noise?

Knowledge of the term structure of interest rates is undeniably important. It enables the price of a stream of cash flows to be determined and is a key element for pricing certain types of derivative instruments including swaps and forward contracts. It is useful in the formation of economic policy. It is used to calibrate the parameters of the stochastic process assumed to govern the evolution of interest rates. Notwithstanding its importance, estimating the term structure of interest rates remains fraught with difficulty. It is usual to produce an estimate of the term structure that is known to result in arbitrage opportunities. This paper suggests a new way which results in a no-arbitrage estimate of the term structure. The origins of our method lie with the implied valuation philosophy that has its roots in the derivative market and has gained popularity there. We show how the spirit of that philosophy can be applied to the estimation of the term structure. The goal in this paper is to uncover the discount function implicit in the prices and cash flows of bonds, and to infer the implicit selection criterion employed. It is common practice to use only straight bonds to estimate the term structure and to throw out of the sample the bonds with embedded options, resulting in the loss of information and an estimate that is quite likely inaccurate. We will show that discarding this sort of information when estimating the term structure creates the illusion of a puzzle -- the illusion of arbitrage opportunities. This puzzle is apparently negatively valued options implicit in the government bonds of three countries. The approach used for term structure estimation in this paper allows the researcher to harness the information contained in government bonds with embedded options and results in an arbitrage-free estimate of the term structure.

Volatility structures of forward rates and the dynamics of the term structure: a multifactor case

For general volatility structures for forward rates, the evolution of interest rates may not be Markovian and the entire path may be necessary to capture the dynamics of the term structure. This article identifies conditions on the volatility structure of forward rates that permit the dynamics of the term structure to be represented by a finite-dimensional state variable Markov process. In the deterministic volatility case, we interpret then-factor model as a sum ofn unidimensional models.

223052 (E51) Modelling the evolution of interest rates: The key to DFA asset models : Venter G.G.,Casualty Actuarial Society Forum, volume 2, 1997, pp 135–164

223052 (E51) Modelling the evolution of interest rates: The key to DFA asset models : Venter G.G.,Casualty Actuarial Society Forum, volume 2, 1997, pp 135–164

The Benefits of Dynamically Hedging the Toronto 35 Stock Index

AbstractA growing number of studies reveal that the performance of dynamic hedging strategies tends to vary across markets, producing large percentage reductions in variance in some and seemingly small reductions in others, relative to constant hedges. This paper examines the hedging effectiveness of Toronto 35 index futures and shows that the application of a dynamic strategy based on a general, bivariate GARCH(1,1) process yields economically significant in‐sample and out‐of‐sample improvements in risk reduction, compared to static hedging strategies.RésuméUn nombre grandissant d 'études révèle que la performance de stratégies de contrepartie dynamiques varie d'un marché à l'autre, produisant dans certains cas des pourcentages de réduction de variance appréciables et, dans d'autres cas, de faibles réductions de variance par rapport à la stratégie statique. Cet article examine l'ef‐ficacité de contrepartie du contrat à terme boursier sur l'indice Toronto 35 et démontre que l'application d'une stratégie dynamique reposant sur un modele GARCH(1,1) bivarié général permet de reduire la variance defaçon significative, sur le plan économique, par rapport au modèle de contrepartie statique et ce, aussi bien à l'interieur qu'à l'extérieur de l'échantillon.

VOLATILITY STRUCTURES OF FORWARD RATES AND THE DYNAMICS OF THE TERM STRUCTURE1

For general volatility structures for forward rates, the evolution of interest rates may not be Markovian and the entire path may be necessary to capture the dynamics of the term structure. This article identifies conditions on the volatility structure of forward rates that permit the dynamics of the term structure to be represented by a two‐dimensional state variable Markov process. the permissible set of volatility structures that accomplishes this goal is shown to be quite large and includes many stochastic structures. In general, analytical characterization of the terminal distributions of the two state variables is unlikely, and numerical procedures are required to value claims. Efficient simulation algorithms using control variates are developed to price claims against the term structure.

Duration measures, immunization, and utility maximization

This paper explores the conditions under which a risk averse investor behaves like an immunizer in choosing the maturity structure of a balance sheet. The setting is similar to Grove's study in that the liabilities are assumed fixed but differs in the assumed evolution of interest rates. (M.A. Grove, On duration and the optimal maturity structure of the balance sheet, Bell Journal of Economics and Management Science 5 (1974) 696–709.) It transpires that the circumstances under which a risk averse investor behave like an immunizer are not as limited as concluded in Grove's study. The model thus explains the extensive use of immunization by the business community.