This book puts numerical methods into action for the purpose of solving concrete problems arising in quantitative finance.

Part one develops a comprehensive toolkit including Monte Carlo simulation, numerical schemes for partial differential equations, stochastic optimization in discrete time, copula functions, transform-based methods and quadrature techniques. The content originates from class notes written for courses on numerical methods for finance and exotic derivative pricing held by the authors since the year 2000.

Part two proposes eighteen self-contained cases covering model simulation, derivative valuation, dynamic hedging, portfolio selection, risk management, statistical estimation and model calibration. It encompasses a wide variety of problems arising in markets for equity, interest rates, credit risk, energy and exotic derivatives.

Each case introduces a problem, develops a detailed solution and illustrates empirical results.

Proposed algorithms are implemented using either Matlab® or Visual Basic for Applications® in collaboration with contributors

• Fills a gap in the current published literature by delivering a case-study collection together with a self-contained course on major numerical methods developed and used by the finance industry
• Learning-by-doing approach: all steps detailed in a self-contained way
• Covers a range of numerical methods
• Blends theoretical presentation and practical implementations
• Originality in the choice of cases
• Provides detailed algorithm and the corresponding code