Jozsef Abaffy

Criteria for transforming a Z-matrix into an M-matrix

A characterization of M-matrices is given by means of a special algorithm in the ABS class for linear systems. The effects of changes in the entries of the coefficient matrix are investigated. An application to the classical static Leontief and Sraffa input- output economic model is presented together with numerical results on a real case using an IBM 3090 200VF.

A nonparametric model for analysis of the EURO bond market

The goal of this paper is to analyse by statistical methods the positions of individual countries within the EURO bond market. To this purpose we assume that each of the individual yield curves equals the sum of a common effect curve and of a country-specific one, interpreted as a spread. This allows to analyse the position of the countries by a two-stage nonparametric regression model. In addition, we provide a nonparametric bootstrap test. Both the estimated regression curves and the test indicate significant differences among European Monetary Union countries. A method for quantification of these differences is designed.

Perturbations of M-matrices via ABS methods and their applications to input-output analysis

Some properties of M-matrices are investigated in order to analyze the closure of the class with respect to perturbations introduced in the matrix. An algorithm is derived by means of the implicit Gauss-Cholesky algorithm in the ABS class for linear systems: a lower estimation of the solution of linear system Ax = b, where A is an M-matrix, and the solutions of the leading principal subsystems are available at each iteration step for a total number of multiplications of order O(n^33). The algorithm also tests whether a Z-matrix is an M-matrix and the effects of changes in the entries of the coefficient matrix during the execution are investigated as well. The number of the extra multiplications, in general, is less than those needed by the Gaussian elimination. Finally, an application to the open Leontief static input-output (I-O) model is presented together with numerical results on a real case using the IBM 3090 200VF computer.

Extensions of the Ho and Lee interest-rate model to the multinomial case

The paper presents a state dependent multinomial model of intertemporal changes in the term structure of interest rates. The model is a one-factor interest-rate model within the Markov family models for short-term interest rate and it extends the Ho and Lee [J. Finance XLI (5) (1986) 1001] binomial model. We derive the theoretical basis of the multinomial model, suggest a computational framework to evaluate the models parameters and investigate the suitability of the model for the Italian market.

Performance Evaluation of Algorithms for Black-Derman-Toy Lattice

Within the framework of sensitivity of the optimal value of the portfolio management problem described in Dupaeova and Bertocchi (1996), Dupaeova and Bertocchi (1997) with respect to lattice calibration, we compare Bjerksund and Stensland approximation algorithm, Kang Pan-Zenios algorithm and a modified Kang Pan-Zenios algorithm to generate short-rate interest rates tree according to Black-Derman-Toy model. Numerical testing of the behaviour of the three algorithms are given. The necessary inputs for Black-Derman-Toy model are yield curve and log-yield volatilities: we provide an evidence on the relatively large sensitivity of the parameters of the fitted lattice on the chosen volatility curve. The reported numerical experience is based on data from the Italian bond market.