Bücher der Reihe Springer Finance Textbooks

This work is aimed at an audience with asound mathematical background wishing to leam about the rapidly expanding field of mathematical finance. Its content is suitable particularly for graduate students in mathematics who have a background in measure theory and prob ability. The emphasis throughout is on developing the mathematical concepts re- quired for the theory within the context of their application. No attempt is made to cover the bewildering variety of novel (or 'exotic') financial instru- ments that now appear on the derivatives markets; the focus throughout remains on a rigorous development of the more basic options that lie at the heart of the remarkable range of current applications of martingale theory to financial markets. The first five chapters present the theory in a discrete-time framework. Stochastic calculus is not required, and this material should be accessible to anyone familiar with elementary probability theory and linear algebra. The basic idea of pricing by arbitrage (or, rather, by nonarbitrage) is presented in Chapter 1. The unique price for a European option in a single- period binomial model is given and then extended to multi-period binomial models. Chapter 2 intro duces the idea of a martingale measure for price pro- cesses. Following a discussion of the use of self-financing trading strategies to hedge against trading risk, it is shown how options can be priced using an equivalent measure for which the discounted price process is a mar- tingale.

Yielding new insights into important market phenomena like asset price bubbles and trading constraints, this is the first textbook to present asset pricing theory using the martingale approach (and all of its extensions).

This book examines financial modeling and computational finance from a BSDE perspective, presenting a unified view of the pricing and hedging theory across all asset classes as well as a review of quantitative finance tools.

This book contains a comprehensive account of pricing models of financial derivatives. It covers risk neutral valuation theory, martingale measure, and tools in stochastic calculus required for the understanding of option pricing theory.

This book describes the modelling of prices of ?nancial assets in a simple d- crete time, discrete state, binomial framework. The basic building block in our book is the one-step binomial model where a known price today can take one of two possible values at a future time, which might, for example, be tomorrow, or next month, or next year.

This encyclopedic, detailed resource covers all the steps of one-period allocation from the foundations to the most advanced developments. It includes a large number of figures and examples as well as real trading and asset management case studies.

"Deals with pricing and hedging financial derivatives.... Computational methods are introduced and the text contains the Excel VBA routines corresponding to the formulas and procedures described in the book.

"A wonderful display of the use of mathematical probability to derive a large set of results from a small set of assumptions.

Developed for the professional Master's program in Computational Finance at Carnegie Mellon, the leading financial engineering program in the U.S. Has been tested in the classroom and revised over a period of several yearsExercises conclude every chapter;

Stochastic processes of common use in mathematical finance are presented in this book, which interlaces financial concepts and instruments such as arbitrage opportunities, option pricing and default risk with Brownian motion and Levy and diffusion processes.

A presentation of classical asset pricing theory, this textbook is the only one to address the economic foundations of financial markets theory from a mathematically rigorous standpoint and to offer a self-contained critical discussion based on empirical results.

This second edition - completely up to date with new exercises - provides a comprehensive and self-contained treatment of the probabilistic theory behind the risk-neutral valuation principle and its application to the pricing and hedging of financial derivatives.

Changing interest rates constitute one of the major risk sources for banks, insurance companies, and other financial institutions. Modeling the term-structure movements of interest rates is a challenging task. This volume gives an introduction to the mathematics of term-structure models in continuous time. LIBOR market models;