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2. Computing stable numerical solutions for multidimensional American option pricing problems: a semi-discretization approach

Author

Company, Rafael, Egorova, Vera, Jódar, Lucas, and Soleymani, Fazlollah

Subjects
Quantitative Finance - Pricing of Securities, Mathematics - Analysis of PDEs, Mathematics - Numerical Analysis, 65M06, 65M12, 65M20
Abstract

The matter of the stability for multi-asset American option pricing problems is a present remaining challenge. In this paper a general transformation of variables allows to remove cross derivative terms reducing the stencil of the proposed numerical scheme and underlying computational cost. Solution of a such problem is constructed by starting with a semi-discretization approach followed by a full discretization using exponential time differencing and matrix quadrature rules. To the best of our knowledge the stability of the numerical solution is treated in this paper for the first time. Analysis of the time variation of the numerical solution with respect to previous time level together with the use of logarithmic norm of matrices are the basis of the stability result. Sufficient stability conditions on step sizes, that also guarantee positivity and boundedness of the solution, are found. Numerical examples for two and three asset problems justify the stability conditions and prove its competitiveness with other relevant methods., Comment: 8 figures, 5 tables

Published
2017

7. Modelling Human Behaviour in the Digital Era: Economic and Social Impacts

Author

de la Poza Elena and Jódar Lucas

Subjects
digitalisation, behaviour, socio-economic impact, robotisation, hyper connection era, metric criteria, performance assessment, o30, o31, j6, l2, Business, HF5001-6182
Abstract

This paper critically analyses the implications the digitalisation process has on individuals and organization ‘s behaviour. The digital era has positive aspects such as the access to information on real time from almost any geographical place combined with the shorten the length of time of processes. In addition, new economic trends and paradigms emerge in the digital era. However, we cannot deny the existence of negative or at least unexpected aspects of the digitalization. This work highlights some of the most alarming aspects of digitization that require the attention and implementation of measures by public authorities to prevent from the collateral damages the digitalisation can produce on citizenship well-being.

Published
2019
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9. Numerical Analysis of Novel Finite Difference Methods

Author

Company, Rafael, Egorova, Vera N., El Fakharany, Mohamed, Jódar, Lucas, Soleymani, Fazlollah, Bock, Hans Georg, Series editor, de Hoog, Frank, Series editor, Friedman, Avner, Series editor, Gupta, Arvind, Series editor, Nachbin, André, Series editor, Ozawa, Tohru, Series editor, Pulleyblank, William R., Series editor, Rusten, Torgeir, Series editor, Santosa, Fadil, Series editor, Seo, Jin Keun, Series editor, Tornberg, Anna-Karin, Series editor, Ehrhardt, Matthias, editor, Günther, Michael, editor, and ter Maten, E. Jan W., editor

Published
2017
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10. Mathematical Modelling in Engineering & Human Behaviour 2018

Author

Rodríguez, Luis Acedo, Jódar, Lucas, and Carlos Cortés, Juan

Abstract

This book includes papers in cross-disciplinary applications of mathematical modelling: from medicine to linguistics, social problems, and more. Based on cutting-edge research, each chapter is focused on a different problem of modelling human behaviour or engineering problems at different levels. The reader would find this book to be a useful reference in identifying problems of interest in social, medicine and engineering sciences, and in developing mathematical models that could be used to successfully predict behaviours and obtain practical information for specialised practitioners. This book is a must-read for anyone interested in the new developments of applied mathematics in connection with epidemics, medical modelling, social issues, random differential equations and numerical methods.

Published
2019

11. Closed form analytic solutions for dilogarithmic double integrals

Author

Tung, Michael M. and Jódar, Lucas

Subjects
Mathematical Physics, High Energy Physics - Phenomenology
Abstract

This note presents techniques to analytically solve double integrals of the dilogarithmic type which are of great importance in the perturbative treatment of quantum field theory. In our approach divergent integrals can be calculated similar to their convergent counterparts after identifying and isolating their singular parts., Comment: plain TeX, 6 pages, 3 figures, to appear in Appl. Math. Lett

Published
2004
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31. Solving Initial and Two-Point Boundary Non-Monic Second Order Difference Matrix Problems without Increasing the Data Dimension

Author

Jódar, Lucas, Byrnes, Christopher I., editor, Amari, S.-I., editor, Anderson, B. D. O., editor, Åström, Karl Johan, editor, Aubin, Jean-Pierre, editor, Banks, H. T., editor, Baras, John S., editor, Bensoussan, A., editor, Burns, John, editor, Chen, Han-Fu, editor, Davis, M. H. A., editor, Fleming, Wendell, editor, Fliess, Michel, editor, Glover, Keith, editor, Hinrichsen, Diederich, editor, Isidori, Alberto, editor, Jakubczyk, B., editor, Kimura, Hidenori, editor, Krener, Arthur J., editor, Kunita, H., editor, Kurzhansky, Alexandre, editor, Kushner, Harold J., editor, Lindquist, Anders, editor, Manitius, Andrzej, editor, Martin, Clyde F., editor, Mitter, Sanjoy, editor, Picci, Giorgio, editor, Pshenichnyj, Boris, editor, Sussmann, H. J., editor, Tarn, T. J., editor, Tikhomirov, V. M., editor, Varaiya, Pravin P., editor, Willems, Jan C., editor, Wonham, W. M., editor, Conte, G., Perdon, A. M., and Wyman, B.

Published
1991
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45. A front‐fixing method for American option pricing on zero‐coupon bond under the Hull and White model.

Author

Company, Rafael, Egorova, Vera N., Jódar, Lucas, and Peris, Jorge

Subjects
BOND prices, PARTIAL differential equations, REPAIRING, FINITE difference method
Abstract

A new efficient numerical method is proposed for valuation of American option on zero‐coupon bond using Hull and White model. By applying the front‐fixing transformation suggested by Holmes and Yang, the original free boundary problem is transformed into a new fixed boundary partial differential equation (PDE) problem, where the optimal stopping boundary is one of the unknowns of the problem. The numerical finite difference scheme for the transformed problem is constructed. Stability and convergence rate is studied empirically. Numerical simulation of the computation of both the option price and the optimal stopping boundary are illustrated with examples and the comparison with the Hull and White tree method. [ABSTRACT FROM AUTHOR]

Published
2022
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