Mathematics of the Financial Markets

Mathematics of the Financial Markets Financial Instruments and Derivatives Modeling, Valuation and Risk Issues "Alain Ruttiens has the ability to turn extremely complex concepts and theories into very easy to understand notions. I wish I had read his book when I started my career!" Marco Dion, Global Head of Equity Quant Strategy, J.P. Morgan "The financial industry is built on a vast collection of financial securities that can be valued and risk profiled using a set of miscellaneous mathematical models. The comprehension of these models is fundamental to the modern portfolio and risk manager in order to achieve a deep understanding of the capabilities and limitations of these methods in the approximation of the market. In his book, Alain Ruttiens exposes these models for a wide range of financial instruments by using a detailed and user friendly approach backed up with real-life data examples. The result is an excellent entry-level and reference book that will help any student and current practitioner up their mathematical modeling skills in the increasingly demanding domain of asset and risk management." Virgile Rostand, Consultant, Toronto ON "Alain Ruttiens not only presents the reader with a synthesis between mathematics and practical market dealing, but, more importantly a synthesis of his thinking and of his life." René Chopard, CEO, Centro di Studi Bancari Lugano, Vezia / Professor, Università dell'Insubria, Varese "Alain Ruttiens has written a book on quantitative finance that covers a wide range of financial instruments, examples and models. Starting from first principles, the book should be accessible to anyone who is comfortable with trading strategies, numbers and formulas." Dr Yuh-Dauh Lyuu, Professor of Finance & Professor of Computer Science & Information Engineering, National Taiwan University

Foreword by A.G. MALLIARIS, Loyola University, Chicago xi Main Notations xiii Introduction xv PART I THE DETERMINISTIC ENVIRONMENT 1 Prior to the Yield Curve: Spot and Forward Rates 3 2 The Term Structure or Yield Curve 13 3 Spot Instruments 23 4 Equities and Stock Indexes 47 5 Forward Instruments 75 6 Swaps 91 7 Futures 119 PART II THE PROBABILISTIC ENVIRONMENT 8 The Basis of Stochastic Calculus 147 9 Other Financial Models: From ARMA to the GARCH Family 165 10 Option Pricing in General 175 11 Options on Specific Underlyings and Exotic Options 209 12 Volatility and Volatility Derivatives 237 13 Credit Derivatives 257 14 Market Performance and Risk Measures 275 15 Beyond the Gaussian Hypothesis: Potential Troubles with Derivatives Valuation 303 Bibliography 319 Index 323