Implementing Models in Quantitative Finance

Introduction This book presents and develops major numerical methods currently used for solving problems arising in quantitative ?nance. Our presentation splits into two parts. Part I is methodological, and offers a comprehensive toolkit on numerical me- ods and algorithms. This includes Monte Carlo simulation, numerical schemes for partial differential equations, stochastic optimization in discrete time, copula fu- tions, 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. R We provide algorithms implemented using either Matlab or Visual Basic for R Applications (VBA). Several codes are made available through a link accessible from the Editor’s web site. Origin Necessity is the mother of invention and, as such, the present work originates in class notes and problems developed for the courses “Numerical Methods in Finance” and “Exotic Derivatives” offered by the authors at Bocconi University within the Master in Quantitative Finance and Insurance program (from 2000–2001 to 2003–2004) and the Master of Quantitative Finance and Risk Management program (2004–2005 to present).

Gianluca Fusai is Associate Professor in Financial Calculus at Università degli Studi del Piemonte Orientale (Italy) and a Research Associate at Financial Options Research Center, Univeristy of Warwick. He holds a Ph.D in Finance from the Warwick Business School and a MS in Statistics and Operational Research from University of Essex, UK. His research interest are Financial Engineering, Numerical Methods, Portfolio Selection, and Financial Statistics. On this topics he has published in journals like Journal of Computational Finance, Risk, Annals of Applied Probability, International Journal of Theoretical and Applied Finance. He has worked as a consultant in the private sector (Mediolanum Assicurazioni, Selenia Luxco, Nike Consulting, Software Company, Equitable House).

Andrea Roncoroni is Associate Professor of Finance at ESSEC Business School (Paris-Singapore), Senior Lecturer at Bocconi University (Milan), and Co-director of the Master in Energy Finance at MIP - Politecnico di Milano. He holds PhDs in Applied Mathematics and in Finance. His research interests cover Energy and Commodity Finance, Financial Modeling, Risk Management and Derivative Structuring. He consults for private companies and lectures for private and public institutions (International Energy Agency, Italian Stock Exchange, Italian Energy Authority, Italian Power Exchange, University Paris Dauphine, University of Oslo). He regularly publishes in academic journals (J.of Business, J.of Banking and Finance, Intl.J.of Business).