Quantitative Finance

Presents a multitude of topics relevant to the quantitative finance community by combining the best of the theory with the usefulness of applications.

Written by accomplished teachers and researchers in the field, this book presents quantitative finance theory through applications to specific practical problems and comes with accompanying coding techniques in R and MATLAB, as well as some generic pseudo-algorithms relevant to modern finance. It also offers over 300 examples and exercises that are appropriate for the beginning student as well as the practitioner in the field.

The Quantitative Finance book is divided into four parts. Part One begins by providing readers with the theoretical backdrop needed from probability and stochastic processes. Useful finance concepts used throughout the book are also presented.

In Part Two of the book, the classical Black-Scholes-Merton model is introduced in a uniquely accessible and understandable way. Implied volatility as well as local volatility surfaces are discussed. Solutions to Partial Differential Equations (PDE), wavelets, and Fourier transforms are presented. Several methodologies for pricing options, namely tree methods, finite difference method, and Monte Carlo simulation methods, are also discussed. This part concludes with a discussion on stochastic differential equations (SDEs).

The third part of this book delves into several new and advanced models from current literature, such as general Lévy processes, nonlinear PDEs for stochastic volatility models in a transaction fee market, PDEs in a jump-diffusion with stochastic volatility models, and factor and copulas models.

In Part Four, the book concludes with a solid presentation of the typical topics in fixed income securities and derivatives. Models for pricing bonds, marketable securities, credit default swaps (CDS), and securitizations are discussed.

• Classroom-tested over a three-year period with the input of students and experienced practitioners.
• Emphasises the volatility of financial analyses and interpretations.
• Weaves theory with application throughout the book.
• Utilises R and MATLAB software programs.
• Presents pseudo-algorithms for readers who do not have access to any particular programming system.
• Supplemented with an extensive author-maintained website that includes helpful teaching hints, datasets, software programs, and additional content.

Quantitative Finance is an ideal textbook for upper-undergraduate and beginning graduate students in statistics, financial engineering, quantitative finance, and mathematical finance programmes. It will also appeal to practitioners in the same fields.