Gloria M. Soto

Immunization Derived from a Polynomial Duration Vector in the Spanish Bond Market

This paper focuses on the Spanish government debt market in an attempt to evaluate the immunization performance of the polynomial duration model of Chambers and Carleton (Chambers, D.R., Carleton, W.T., 1988. A generalized approach to duration. In: Chen, A.H. (Ed.), Research in Finance, vol. 7, JAI Press, Greenwich, pp. 163-181), in default-free and option-free fixed-income portfolios and to ascertain whether traditional convexity is an earnings-generating element. Empirical tests show that three constraints, namely those related to the level, slope and curvature of term structure shifts, are necessary to guarantee a return close to the target. The only exception to this rule is found in portfolios including an asset that matures near the horizon date, in which classical immunization performs properly.

Linear and nonlinear interest rate exposure in Spain

Purpose - This paper aims to carry out a comprehensive analysis of the influence of interest rate risk on Spanish firms at the industry level. Design/methodology/approach - The methodology employed has its origin in the two-index linear regression model proposed by Stone. This traditional interest rate exposure model has been extended in this paper to allow for a nonlinear exposure component as well as the presence of asymmetric behaviour in the exposure pattern. Findings - Interest rate exposure is not homogeneous for all the Spanish industries. In line with other markets, highly leveraged industries (construction and real estate), regulated industries (electrical and utilities), and banking industry are the most interest rate sensitive. Nevertheless, the interest rate exposure of Spanish firms also shows some distinctive features due to the peculiar structure of the Spanish market. It is also documented that the classical linear exposure profile prevails over the nonlinear and asymmetric exposure patterns, and that the introduction of the euro seems to have weakened the degree of interest rate risk. Practical implications - The evidence presented in this paper can be used as input in decision making by corporate managers, investors, and regulators interested in assessing the impact of interest rate risk at the sector level for hedging, portfolio management, or risk assessment purposes. Originality/value - This is the first paper which tackles the analysis of the impact of interest rate risk on Spanish firms, taking into account not only the standard linear interest rate exposure profile but also the nonlinear one. The results found in the Spanish case reveal the existence of particularities which might also be present in countries immersed in a process of dramatic economic transformations similar to that experienced by Spain over the past two decades. This is the case of the Central and Eastern European countries which recently joined the European Union.

Generalized M-Vector Models for Hedging Interest Rate Risk

This paper generalizes the M-square and M-vector models (Fong and Fabozzi [1985] and Nawalkha and Chambers [1997]) by using a Taylor series expansion of the bond return function with respect to simple polynomial functions of the cash flow maturities. The classic M-vector computes the weighted averages of the distance between the maturity of each cash flow and the portfolio horizon, raised to integer powers (e.g., (t - H)^1, (t - H)^2, (t - H)^3, etc.). Implementation of the new approach involves computing the weighted averages of the distance between some polynomial function of the maturity of each cash flow and that of the portfolio horizon, raised to integer powers (e.g., (t^0.5 - H^0.5)^1, (t^0.5 - H^0.5)^2, (t^0.5 - H^0.5)^3, etc.). We test six different generalized M-vector models corresponding to six different polynomial functions. It is shown that polynomial functions of lower power (i.e., 0.25 or 0.5) provide significantly enhanced protection from interest rate risk, when higher-order generalized M-vector models are used.

Duration models and IRR management: A question of dimensions?

This paper compares the immunization performance of alternative single and multiple factor duration models, using Spanish government bond data, over 1, 2 and 3-year horizons. The aim is to assess whether the success of duration-matching strategies is primarily attributable to the particular model chosen or to the number of risk factors considered. Empirical tests show that: (i) traditional immunization is easily bettered by more realistic strategies; (ii) the number of risk factors considered has a greater influence on the result than the particular model chosen; and (iii) three-factor immunization strategies offer the highest immunization benchmarks.

Pricing American Interest Rate Options under the Jump-Extended Vasicek Model

This paper shows how to price American interest rate options under the exponential jumps-extended Vasicek model. We modify the Gaussian jump-diffusion tree of Amin [1993] and apply to the exponential jumps-based short rate process under the Vasicek-EJ model. The tree is truncated at both ends to allow fast computation of option prices. We also consider the time-inhomogeneous version of this model, denoted as the Vasicek-EJ++ model that allows exact calibration to the initially observable bond prices. Our simulations show fast convergence of European option prices obtained using the jump-diffusion tree, to those obtained using the Fourier inversion method and the cumulant expansion method.

Managing Interest Rate Risk: The Next Challenge?

Are the managers of financial institutions ready for the small but increasingly significant risk of inflation in the near future, due to the unprecedented fiscal and monetary responses of the U.S. government to prevent an economic collapse? This paper addresses this important issue by reviewing important findings in the area of interest rate risk management. We discuss five classes of models in the fixed income literature that deal with hedging the risk of large, non-parallel yield curve shifts. These models are given as M-Absolute/M-Square models, duration vector models, key rate duration models, principal component duration models, and extensions of these models for fixed income derivatives, for valuing and hedging bonds, loans, demand deposits, and other fixed income instruments. These models can be used for designing various hedging strategies such as portfolio immunization, bond index replication, duration gap management, and contingent immunization, to protect against changes in the height, slope, and curvature of the yield curve. We argue that the current regulatory models proposed by the U.S. Federal Reserve, the Office of Thrift Supervision, and the Bank of International Settlements, may understate the true interest rate risk exposure of financial institutions, if sharp increases in interest rates lead to higher default risk and quickening of the pace of deposit withdrawals.

Term Structure Estimation

The term structure of interest rates gives the relationship between the yield on an investment and the term to maturity of the investment. Since the term structure is typically measured using default-free, continuously-compounded, annualized zero-coupon yields, it is not directly observable from the published coupon bond prices and yields. This paper focuses on how to estimate the default-free term structure of interest rates from bond data using three methods: the bootstrapping method, the McCulloch cubic-spline method, and the Nelson and Siegel method. Nelson and Siegel method is shown to be more robust than the other two methods. The results of this paper can be implemented using user-friendly Excel spreadsheets.

Using Principal Component Analysis to Explain Term Structure Movements: Performance and Stability

This paper evaluates the performance of a kind of interest rate model that has increasingly been attracting the attention of the financial industry in recent years and which relies on principal component analysis to extract risk factors. Focusing on the Spanish bond market, our empirical analysis reveals that interest rate movements can be summarized by three principal components, related to the level, the steepness and the curvature of the yield curve. This three-principal component model is able to offer a balanced explanation of interest rate shocks and bond returns across maturities and overcomes typical one- and two-factor interest rate models. However, our results also reveal some variations with time in the principal components that point to the need to recognize the dynamic volatility structure of interest rates.

Linear and Nonlinear Interest Rate Exposure of Spanish Firms

This paper carries out a comprehensive analysis of the interest rate risk borne by the Spanish firms on a sector basis. The traditional linear interest rate exposure model has been extended to allow for the possibility of a nonlinear exposure component as well as the presence of asymmetric behaviour in the exposure pattern. The obtained results show a significant interest rate exposure for some sectors, especially with regard to changes in the long-term interest rates. Moreover, it is documented that the linear exposure profile prevails over the asymmetric and nonlinear exposure patterns. In particular, the Construction sector is the sector that shows the highest incidence of interest rate risk in the Spanish case.

Multifactor Models for Managing Interest Rate Risk

How do the managers of financial institutions hedge against the effects of non-parallel yield curve shifts? This paper addresses this important issue by reviewing the important findings in the area of interest rate risk management over the past two decades. We discuss four classes of models in the fixed income literature that deal with hedging the risk of large, non-parallel yield curve shifts. These models are given as M-Absolute/M-Square models, duration vector models, key rate duration models, and principal component duration models. These models can be used for designing various passive strategies such as portfolio immunization, bond index replication, and duration gap management; and hybrid strategies (i.e., active/passive) such as targeted yield curve shifts speculation (based on change in either the height, and/or the slope, and/or the curvature of the yield curve) and contingent immunization.