Quantitative Finance

This book falls broadly in the area of financial mathematics. It presents a multitude of topics that are relevant to the quantitative finance community. Experts in teaching and active in research, the authors aim to discuss theory in the context of applications to specific practical problems. The book is complete with different coding techniques in R and MATLAB and generic pseudo-algorithms to modern finance. Starting with the theoretical backdrop needed from probability and stochastic processes and the description of financial instruments priced throughout the book, the classical Black-Scholes-Merton model is, then, presented in a uniquely accessible and understandable way. Implied volatility, local volatility surfaces, and general methods of inverting partial differential equations (PDE’s) are, then, discussed. Two fundamental ways of calculating the price of options and other derivatives are showcased along with a solid presentation of the usual topics in fixed income derivatives, classical models, portfolio management, and hedging portfolios. The book concludes with several new and advanced models from current literature such as nonlinear PDE’s for stochastic volatility models in a transaction fee market and PDE’s in a jump-diffusion with stochastic volatility models. There are over 300 examples and exercises that are appropriate for the beginning learner and the practicing financier.