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Record Nr. |
UNISA996202349503316 |
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Autore |
Brandimarte Paolo |
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Titolo |
Numerical methods in finance and economics : a MATLAB-based introduction / / Paolo Brandimarte |
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Pubbl/distr/stampa |
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Hoboken, New Jersey : , : Wiley Interscience, , 2006 |
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©2006 |
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ISBN |
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1-118-62557-9 |
1-280-72159-6 |
9786610721597 |
0-470-08049-3 |
0-470-08048-5 |
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Edizione |
[2nd ed.] |
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Descrizione fisica |
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1 online resource (697 p.) |
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Collana |
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Altri autori (Persone) |
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Disciplina |
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Soggetti |
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Finance - Statistical methods |
Economics - Statistical methods |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Rev. ed. of: Numerical methods in finance. 2002. |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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Numerical Methods in Finance and Economics: A MATLAB-Based Introduction; Contents; Preface to the Second Edition; From the Preface to the First Edition; Part I Background; 1 Motivation; 1.1 Need for numerical methods; 1.2 Need for numerical computing environments: why MATLAB?; 1.3 Need for theory; For further reading; References; 2 Financial Theory; 2.1 Modeling uncertainty; 2.2 Basic financial assets and related issues; 2.2.1 Bonds; 2.2.2 Stocks; 2.2.3 Derivatives; 2.2.4 Asset pricing, portfolio optimization, and risk management |
2.3 Fixed-income securities: analysis and portfolio immunization2.3.1 Basic theory of interest rates: compounding and present value; 2.3.2 Basic pricing of fixed-income securities; 2.3.3 Interest rate sensitivity and bond portfolio immunization; 2.3.4 MATLAB functions to deal with fixed-income securities; 2.3.5 Critique; 2.4 Stock portfolio optimization; 2.4.1 Utility theory; 2.4.2 Mean-variance portfolio optimization; 2.4.3 MATLAB functions to deal with mean-variance portfolio optimization; 2.4.4 Critical remarks; 2.4.5 Alternative risk |
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measures: Value at Risk and quantile-based measures |
2.5 Modeling the dynamics of asset prices2.5.1 From discrete to continuous time; 2.5.2 Standard Wiener process; 2.5.3 Stochastic integrals and stochastic differential equations; 2.5.4 Ito's lemma; 2.5.5 Generalizations; 2.6 Derivatives pricing; 2.6.1 Simple binomial model for option pricing; 2.6.2 Black-Scholes model; 2.6.3 Risk-neutral expectation and Feynman-Kac formula; 2.6.4 Black-Scholes model in MATLAB; 2.6.5 A few remarks on Black-Scholes formula; 2.6.6 Pricing American options; 2.7 Introduction to exotic and path-dependent options; 2.7.1 Barrier options; 2.7.2 Asian options |
2.7.3 Lookback options2.8 An outlook on interest-rate derivatives; 2.8.1 Modeling interest-rate dynamics; 2.8.2 Incomplete markets and the market price of risk; For further reading; References; Part II Numerical Methods; 3 Basics of Numerical Analysis; 3.1 Nature of numerical computation; 3.1.1 Number representation, rounding, and truncation; 3.1.2 Error propagation, conditioning, and instability; 3.1.3 Order of convergence and computational complexity; 3.2 Solving systems of linear equations; 3.2.1 Vector and matrix norms; 3.2.2 Condition number for a matrix |
3.2.3 Direct methods for solving systems of linear equations3.2.4 Tridiagonal matrices; 3.2.5 Iterative methods for solving systems of linear equations; 3.3 Function approximation and interpolation; 3.3.1 Ad hoc approximation; 3.3.2 Elementary polynomial interpolation; 3.3.3 Interpolation by cubic splines; 3.3.4 Theory of function approximation by least squares; 3.4 Solving non-linear equations; 3.4.1 Bisection method; 3.4.2 Newton's method; 3.4.3 Optimization-based solution of non-linear equations; 3.4.4 Putting two things together: solving a functional equation by a collocation method |
3.4.5 Homotopy continuation methods |
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Sommario/riassunto |
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A state-of-the-art introduction to the powerful mathematical and statistical tools used in the field of financeThe use of mathematical models and numerical techniques is a practice employed by a growing number of applied mathematicians working on applications in finance. Reflecting this development, Numerical Methods in Finance and Economics: A MATLAB?-Based Introduction, Second Edition bridges the gap between financial theory and computational practice while showing readers how to utilize MATLAB?--the powerful numerical computing environment--for financial applications.The aut |
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