A comprehensive introduction to various numerical methods usedin computational finance today
Quantitative skills are a prerequisite for anyone working infinance or beginning a career in the field, as well as riskmanagers. A thorough grounding in numerical methods is necessary,as is the ability to assess their quality, advantages, andlimitations. This book offers a thorough introduction to eachmethod, revealing the numerical traps that practitioners frequentlyfall into. Each method is referenced with practical, real-worldexamples in the areas of valuation, risk analysis, and calibrationof specific financial instruments and models. It features a strongemphasis on robust schemes for the numerical treatment of problemswithin computational finance. Methods covered include PDE/PIDEusing finite differences or finite elements, fast and stablesolvers for sparse grid systems, stabilization and regularizationtechniques for inverse problems resulting from the calibration offinancial models to market data, Monte Carlo and Quasi Monte Carlotechniques for simulating high dimensional systems, and local andglobal optimization tools to solve the minimization problem.