Focusing on recent advances in option pricing under the SABR model, this book shows how to price options under this model in an arbitrage-free, theoretically consistent manner. It extends SABR to a negative rates environment, and shows how to generalize it to a similar model with additional degrees of freedom, allowing simultaneous model calibration to swaptions and CMSs. Since the SABR model is used on practically every trading floor to construct interest rate options volatility cubes in an arbitrage-free manner, a careful treatment of it is extremely important. The book will be of interest to experienced industry practitioners, as well as to students and professors in academia. Aimed mainly at financial industry practitioners (for example quants and former physicists) this book will also be interesting to mathematicians who seek intuition in the mathematical finance.

Focusing on recent advances in option pricing under the SABR model, this book shows how to price options under this model in an arbitrage-free, theoretically consistent manner. It extends SABR to a negative rates environment, and shows how to generalize it to a similar model with additional degrees of freedom, allowing simultaneous model calibration to swaptions and CMSs. Since the SABR model is used on practically every trading floor to construct interest rate options volatility cubes in an arbitrage-free manner, a careful treatment of it is extremely important. The book will be of interest to experienced industry practitioners, as well as to students and professors in academia. Aimed mainly at financial industry practitioners (for example quants and former physicists) this book will also be interesting to mathematicians who seek intuition in the mathematical finance.

Stress-test financial models and price credit instruments with confidence and efficiency using the perturbation approach taught in this expert volume Perturbation Methods in Credit Derivatives: Strategies for Efficient Risk Management offers an incisive examination of a new approach to pricing credit-contingent financial instruments. Author and experienced financial engineer Dr. Colin Turfus has created an approach that allows model validators to perform rapid benchmarking of risk and pricing models while making the most efficient use possible of computing resources. The book provides innumerable benefits to a wide range of quantitative financial experts attempting to comply with increasingly burdensome regulatory stress-testing requirements, including: Replacing time-consuming Monte Carlo simulations with faster, simpler pricing algorithms for front-office quants Allowing CVA quants to quantify the impact of counterparty risk, including wrong-way correlation risk, more efficiently Developing more efficient algorithms for generating stress scenarios for market risk quants Obtaining more intuitive analytic pricing formulae which offer a clearer intuition of the important relationships among market parameters, modelling assumptions and trade/portfolio characteristics for traders The methods comprehensively taught in Perturbation Methods in Credit Derivatives also apply to CVA/DVA calculations and contingent credit default swap pricing.

This book is a substantially revised and expanded edition reflecting major developments in stochastic numerics since the first edition was published in 2004. The new topics, in particular, include mean-square and weak approximations in the case of nonglobally Lipschitz coefficients of Stochastic Differential Equations (SDEs) including the concept of rejecting trajectories; conditional probabilistic representations and their application to practical variance reduction using regression methods; multi-level Monte Carlo method; computing ergodic limits and additional classes of geometric integrators used in molecular dynamics; numerical methods for FBSDEs; approximation of parabolic SPDEs and nonlinear filtering problem based on the method of characteristics. SDEs have many applications in the natural sciences and in finance. Besides, the employment of probabilistic representations together with the Monte Carlo technique allows us to reduce the solution of multi-dimensional problems for partial differential equations to the integration of stochastic equations. This approach leads to powerful computational mathematics that is presented in the treatise. Many special schemes for SDEs are presented. In the second part of the book numerical methods for solving complicated problems for partial differential equations occurring in practical applications, both linear and nonlinear, are constructed. All the methods are presented with proofs and hence founded on rigorous reasoning, thus giving the book textbook potential. An overwhelming majority of the methods are accompanied by the corresponding numerical algorithms which are ready for implementation in practice. The book addresses researchers and graduate students in numerical analysis, applied probability, physics, chemistry, and engineering as well as mathematical biology and financial mathematics.

The book discusses a class of discrete time stochastic growth processes for which the growth rate is proportional to the exponential of a Gaussian Markov process. These growth processes appear naturally in problems of mathematical finance as discrete time approximations of stochastic volatility models and stochastic interest rates models such as the Black-Derman-Toy and Black-Karasinski models. These processes can be mapped to interacting one-dimensional lattice gases with long-range interactions. The book gives a detailed discussion of these statistical mechanics models, including new results not available in the literature, and their implication for the stochastic growth models. The statistical mechanics analogy is used to understand observed non-analytic dependence of the Lyapunov exponents of the stochastic growth processes considered, which is related to phase transitions in the lattice gas system. The theoretical results are applied to simulations of financial models and are illustrated with Mathematica code. The book includes a general introduction to exponential stochastic growth with examples from biology, population dynamics and finance. The presentation does not assume knowledge of mathematical finance. The new results on lattice gases can be read independently of the rest of the book. The book should be useful to practitioners and academics studying the simulation and application of stochastic growth models.

When Bill James published his original Historical Baseball Abstract in 1985, he produced an immediate classic, hailed by the Chicago Tribune as the “holy book of baseball.” Now, baseball's beloved “Sultan of Stats” (The Boston Globe) is back with a fully revised and updated edition for the new millennium. Like the original, The New Bill James Historical Baseball Abstract is really several books in one. The Game provides a century's worth of American baseball history, told one decade at a time, with energetic facts and figures about How, Where, and by Whom the game was played. In The Players, you'll find listings of the top 100 players at each position in the major leagues, along with James's signature stats-based ratings method called “Win Shares,” a way of quantifying individual performance and calculating the offensive and defensive contributions of catchers, pitchers, infielders, and outfielders. And there's more: the Reference section covers Win Shares for each season and each player, and even offers a Win Share team comparison. A must-have for baseball fans and historians alike, The New Bill James Historical Baseball Abstract is as essential, entertaining, and enlightening as the sport itself.

Michael Lewis’s instant classic may be “the most influential book on sports ever written” (People), but “you need know absolutely nothing about baseball to appreciate the wit, snap, economy and incisiveness of [Lewis’s] thoughts about it” (Janet Maslin, New York Times). One of GQ's 50 Best Books of Literary Journalism of the 21st Century Just before the 2002 season opens, the Oakland Athletics must relinquish its three most prominent (and expensive) players and is written off by just about everyone—but then comes roaring back to challenge the American League record for consecutive wins. How did one of the poorest teams in baseball win so many games? In a quest to discover the answer, Michael Lewis delivers not only “the single most influential baseball book ever” (Rob Neyer, Slate) but also what “may be the best book ever written on business” (Weekly Standard). Lewis first looks to all the logical places—the front offices of major league teams, the coaches, the minds of brilliant players—but discovers the real jackpot is a cache of numbers?numbers!?collected over the years by a strange brotherhood of amateur baseball enthusiasts: software engineers, statisticians, Wall Street analysts, lawyers, and physics professors. What these numbers prove is that the traditional yardsticks of success for players and teams are fatally flawed. Even the box score misleads us by ignoring the crucial importance of the humble base-on-balls. This information had been around for years, and nobody inside Major League Baseball paid it any mind. And then came Billy Beane, general manager of the Oakland Athletics. He paid attention to those numbers?with the second-lowest payroll in baseball at his disposal he had to?to conduct an astonishing experiment in finding and fielding a team that nobody else wanted. In a narrative full of fabulous characters and brilliant excursions into the unexpected, Michael Lewis shows us how and why the new baseball knowledge works. He also sets up a sly and hilarious morality tale: Big Money, like Goliath, is always supposed to win . . . how can we not cheer for David?

Interest in Sabermetrics has increased dramatically in recent years as the need to better compare baseball players has intensified among managers, agents and fans, and even other players. The authors explain how traditional measures--such as Earned Run Average, Slugging Percentage, and Fielding Percentage--along with new statistics--Wins Above Average, Fielding Independent Pitching, Wins Above Replacement, the Equivalence Coefficient and others--define the value of players. Actual player statistics are used in developing models, while examples and exercises are provided in each chapter. This book serves as a guide for both beginners and those who wish to be successful in fantasy leagues.

The past 30 years have seen an explosion in the number and variety of baseball books and articles. Following the lead of pioneers Bill James, John Thorn, and Pete Palmer, researchers have steadily challenged the ways we think about player and team performance--and along the way revised what we thought we knew of baseball history. This book by the authors of Understanding Sabermetrics (2008) goes beyond the explanation of new statistics to demonstrate their use in solving some of the more familiar problems of baseball research, such as how to compare players across generations; how to account for the effects of ballparks and rules changes; and how to measure the effectiveness of the sacrifice bunt or the range of the Gold Glove-winning shortstop. Instructors considering this book for use in a course may request an examination copy here.

Preeminent baseball analyst Bill James and ESPN.com baseball columnist Rob Neyer compile information on pitches and their origins, nearly two thousand pitchers, and more in this comprehensive guide. Pitchers, the pitches they throw, and how they throw them—they’re the stuff of constant scrutiny, but there's never been anything like a comprehensive source for such information…until now. Bill James and Rob Neyer spent over a decade compiling the centerpiece of this book, the Pitcher Census, which lists specific information for nearly two thousand pitchers, ranging throughout the history of professional baseball. Their guide also includes a dictionary describing virtually every known pitch, biographies of great pitchers who have been overlooked, and top ten lists for fastballs, spitballs, and everything in between. James and Neyer also weigh in on the debate over pitcher abuse and durability, offer a formula for predicting the Cy Young Award winner, and reveal James’s Pitcher Codes. Learn about the origins and development of baseball’s most important pitches and more knuckleballers and submariners than you ever thought existed! Baseball’s action always starts with the pitchers. Begin to understand them and join in on entertaining debates while having a great deal of fun with the history of the game that captivates so many with this one-of-a-kind guide.