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Numerical Methods and Optimization in Finance

Author

Listed:
  • Gilli, Manfred

    (University of Geneva, Switzerland; and Swiss Finance Institute)

  • Maringer, Dietmar

    (University of Basel and University of Geneva, Switzerland)

  • Schumann, Enrico

    (VIP Value Investment Professionals AG, Switzerland)

Abstract

This book describes computational finance tools. It covers fundamental numerical analysis and computational techniques, such as option pricing, and gives special attention to simulation and optimization. Many chapters are organized as case studies around portfolio insurance and risk estimation problems. In particular, several chapters explain optimization heuristics and how to use them for portfolio selection and in calibration of estimation and option pricing models. Such practical examples allow readers to learn the steps for solving specific problems and apply these steps to others. At the same time, the applications are relevant enough to make the book a useful reference. Matlab and R sample code is provided in the text and can be downloaded from the book's website. Shows ways to build and implement tools that help test ideas Focuses on the application of heuristics; standard methods receive limited attention Presents as separate chapters problems from portfolio optimization, estimation of econometric models, and calibration of option pricing models

Suggested Citation

  • Gilli, Manfred & Maringer, Dietmar & Schumann, Enrico, 2011. "Numerical Methods and Optimization in Finance," Elsevier Monographs, Elsevier, edition 1, number 9780123756626.
    • Handle: RePEc:eee:monogr:9780123756626
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    Keywords

    Acceptance-rejection method; Adaptive expectations; Agent-based modeling; Algorithmic complexity; American option; Approximation; ARMA; Asset selection; Autoregression; Barrier option; Bates Model; Binomial Trees; Bisection; Bootstrap; Boundary conditions; Box-Muller method; Brownian bridge; Calibration of option pricing models; Characteristic function; Computer arithmetic; Condition number; Constant proportion portfolio insurance (CPPI); Constraints; Copula; Crank-Nicolson; Differential Evolution; Direct methods; Direct search; Downside risk; Early exercise; Early exercise boundary; Escrowed dividend model; Experimental design; Explicit method; Extreme value theory; Financial Modeling; Financial Optimization; Finite differences; Fixed point; Gap risk; GARCH; Gauss rules; Gauss-Newton; Gauss-Seidel method; Geometric Brownian motion; Gradient based method; Greeks; Heston model; Historical simulation; Implicit method; Implied volatility; Initial conditions; Interest rate models; Inversion method; Iterative methods; Jacobi method; Least Median of Squares; Least Squares problems; Least Trimmed Squares; Levenberg-Marquardt; Linear correlation; Local Search; Machine precision; Markov chain; Matrix factorization; Metropolis algorithm; Model accuracy; Model evaluation; Model risk; Moving average processes; Nelder-Mead direct search; Nelson-Siegel model; Nelson-Siegel-Svensson model; Newton method; Nonlinear Least Squares; Numerical instability; Numerical integration; Numerical methods in finance; Operation count; Optimization; Optimization heuristics; Option pricing; Particle Swarm Optimization; Portfolio optimization; Portfolios; Pseudo-random numbers; Quadratic programming; Quasi-Monte Carlo; Random number generator; Rank correlation; Risk-reward measures; Robust regression; Root finding; SOR; Sparse matrices; Steepest descent; Term structure models; Threshold Accepting; Unconstrained optimization; Value-at-risk; Volatility clustering; Wiener processes; θ-method;
    All these keywords.

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