An Introduction to the Mathematics of Financial Derivatives, Second Edition, introduces the mathematics underlying the pricing of derivatives. The increased interest in dynamic pricing models stems from their applicability to practical situations: with the freeing of exchange, interest rates, and capital controls, the market for derivative products has matured and pricing models have become more accurate. This updated edition has six new chapters and chapter-concluding exercises, plus one thoroughly expanded chapter. The text answers the need for a resource targeting professionals, Ph.D. students, and advanced MBA students who are specifically interested in financial derivatives. This edition is also designed to become the main text in first year masters and Ph.D. programs for certain courses, and will continue to be an important manual for market professionals and professionals with mathematical, technical, or physics backgrounds.
An Introduction to the Mathematics of Financial Derivatives is a popular, intuitive text that eases the transition between basic summaries of financial engineering to more advanced treatments using stochastic calculus. Requiring only a basic knowledge of calculus and probability, it takes readers on a tour of advanced financial engineering. This classic title has been revised by Ali Hirsa, who accentuates its well-known strengths while introducing new subjects, updating others, and bringing new continuity to the whole. Popular with readers because it emphasizes intuition and common sense, An Introduction to the Mathematics of Financial Derivatives remains the only "introductory" text that can appeal to people outside the mathematics and physics communities as it explains the hows and whys of practical finance problems. Facilitates readers' understanding of underlying mathematical and theoretical models by presenting a mixture of theory and applications with hands-on learning Presented intuitively, breaking up complex mathematics concepts into easily understood notions Encourages use of discrete chapters as complementary readings on different topics, offering flexibility in learning and teaching
This second edition, now featuring new material, focuses on the valuation principles that are common to most derivative securities. A wide range of financial derivatives commonly traded in the equity and fixed income markets are analysed, emphasising aspects of pricing, hedging and practical usage. This second edition features additional emphasis on the discussion of Ito calculus and Girsanovs Theorem, and the risk-neutral measure and equivalent martingale pricing approach. A new chapter on credit risk models and pricing of credit derivatives has been added. Up-to-date research results are provided by many useful exercises.
An Introduction to the Mathematics of Finance: A Deterministic Approach, 2e, offers a highly illustrated introduction to mathematical finance, with a special emphasis on interest rates. This revision of the McCutcheon-Scott classic follows the core subjects covered by the first professional exam required of UK actuaries, the CT1 exam. It realigns the table of contents with the CT1 exam and includes sample questions from past exams of both The Actuarial Profession and the CFA Institute. With a wealth of solved problems and interesting applications, An Introduction to the Mathematics of Finance stands alone in its ability to address the needs of its primary target audience, the actuarial student. Closely follows the syllabus for the CT1 exam of The Institute and Faculty of Actuaries Features new content and more examples Online supplements available: http://booksite.elsevier.com/9780080982403/ Includes past exam questions from The Institute and Faculty of Actuaries and the CFA Institute
The modern subject of mathematical finance has undergone considerable development, both in theory and practice, since the seminal work of Black and Scholes appeared a third of a century ago. This book is intended as an introduction to some elements of the theory that will enable students and researchers to go on to read more advanced texts and research papers. The book begins with the development of the basic ideas of hedging and pricing of European and American derivatives in the discrete (i.e., discrete time and discrete state) setting of binomial tree models. Then a general discrete finite market model is introduced, and the fundamental theorems of asset pricing are proved in this setting. Tools from probability such as conditional expectation, filtration, (super)martingale, equivalent martingale measure, and martingale representation are all used first in this simple discrete framework. This provides a bridge to the continuous (time and state) setting, which requires the additional concepts of Brownian motion and stochastic calculus. The simplest model in the continuous setting is the famous Black-Scholes model, for which pricing and hedging of European and American derivatives are developed. The book concludes with a description of the fundamental theorems for a continuous market model that generalizes the simple Black-Scholes model in several directions.
An elementary introduction to probability and mathematical finance including a chapter on the Capital Asset Pricing Model (CAPM), a topic that is very popular among practitioners and economists. Dr. Roman has authored 32 books, including a number of books on mathematics, such as Coding and Information Theory, Advanced Linear Algebra, and Field Theory, published by Springer-Verlag.
An innovative textbook for use in advanced undergraduate and graduate courses; accessible to students in financial mathematics, financial engineering and economics. Introduction to the Economics and Mathematics of Financial Markets fills the longstanding need for an accessible yet serious textbook treatment of financial economics. The book provides a rigorous overview of the subject, while its flexible presentation makes it suitable for use with different levels of undergraduate and graduate students. Each chapter presents mathematical models of financial problems at three different degrees of sophistication: single-period, multi-period, and continuous-time. The single-period and multi-period models require only basic calculus and an introductory probability/statistics course, while an advanced undergraduate course in probability is helpful in understanding the continuous-time models. In this way, the material is given complete coverage at different levels; the less advanced student can stop before the more sophisticated mathematics and still be able to grasp the general principles of financial economics. The book is divided into three parts. The first part provides an introduction to basic securities and financial market organization, the concept of interest rates, the main mathematical models, and quantitative ways to measure risks and rewards. The second part treats option pricing and hedging; here and throughout the book, the authors emphasize the Martingale or probabilistic approach. Finally, the third part examines equilibrium models--a subject often neglected by other texts in financial mathematics, but included here because of the qualitative insight it offers into the behavior of market participants and pricing.