This book presents and develops major numerical methods currently used for solving problems arising in quantitative finance. Our presentation splits into two parts.
Part I is methodological, and offers a comprehensive toolkit on numerical methods and algorithms. This includes Monte Carlo simulation, numerical schemes for partial differential equations, stochastic optimization in discrete time, copula functions, transform-based methods and quadrature techniques.
Part II is practical, and features a number of self-contained cases. Each case introduces a concrete problem and offers a detailed, step-by-step solution. Computer code that implements the cases and the resulting output is also included.
The cases encompass a wide variety of quantitative issues arising in markets for equity, interest rates, credit risk, energy and exotic derivatives. The corresponding problems cover model simulation, derivative valuation, dynamic hedging, portfolio selection, risk management, statistical estimation and model calibration.