Numerical methods in finance and economics : a MATLAB-based introduction / / Paolo Brandimarte

• Autore: Brandimarte Paolo
• Pubblicazione: Hoboken, New Jersey : , : Wiley Interscience, , 2006; ©2006
• Edizione: 2nd ed.
• Descrizione fisica: 1 online resource (697 p.)
• Disciplina: 332.0151; 515.0285536
• Soggetto topico: Finance - Statistical methods; Economics - Statistical methods
• Soggetto genere / forma: Electronic books.
• Altri autori: BrandimartePaolo
• Note generali: Rev. ed. of: Numerical methods in finance. 2002.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: 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 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
• Sommario/riassunto: 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
• Titolo autorizzato: Numerical methods in finance and economics
• ISBN: 1-118-62557-9; 1-280-72159-6; 9786610721597; 0-470-08049-3; 0-470-08048-5
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910143418803321
• Lo trovi qui: Univ. Federico II
• Serie: Statistics in practice.