Description

Written by leading academics and practitioners in the field of financial mathematics, the purpose of this book is to provide a unique combination of some of the most important and relevant theoretical and practical tools from which any advanced undergraduate and graduate student, professional quant and researcher will benefit. This book stands out from all other existing books in quantitative finance from the sheer impressive range of ready-to-use software and accessible theoretical tools that are provided as a complete package. By proceeding from simple to complex, the authors cover core topics in derivative pricing and risk management in a style that is engaging, accessible and self-instructional. The book contains a wide spectrum of problems, worked-out solutions, detailed methodologies and applied mathematical techniques for which anyone planning to make a serious career in quantitative finance must master. In fact, core portions of the book’s material originated and evolved after years of classroom lectures and computer laboratory courses taught in a world-renowned professional Master’s program in mathematical finance. As a bonus to the reader, the book also gives a detailed exposition on new cutting-edge theoretical techniques with many results in pricing theory that are published here for the first time.

Key Features

*Includes easy-to-implement VB/VBA numerical software libraries *Proceeds from simple to complex in approaching pricing and risk management problems *Provides analytical methods to derive cutting-edge pricing formulas for equity derivatives

Readership

Students in finance programs, particularly financial engineering.

Table of Contents

I Pricing Theory and Risk Management 11 1 Pricing Theory 13 1.1 Single Period, Finite Financial Models . . . . . . . . . . . . . . . . . 16 1.2 Continuous state spaces . . . . . . . . . . . . . . . . . . 24 1.3 Multivariate Continuous Distributions: Basic Tools . . . . . . . . . . 28 1.4 Brownian Motion, Martingales and Stochastic Integrals . . . . . . . . 35 1.5 Stochastic Differential Equations and Ito’s formula . . . . . . . . . . 46 1.6 Geometric Brownian Motion . . .52 1.7 Forwards and European Calls and Puts . . . . . . . . . . . . . . . . . 61 1.8 Static Hedging and Replication of Exotic Payoffs . . . . . . . . . . . 68 1.9 Continuous Time Financial Models . . . . . . . . . . . . . . . . . . . 77 1.10 Dynamic Hedging and Derivative Asset Pricing in Continuous Time . 84 1.11 Hedging with Forwards and Futures . . . . . . . . . . . . . . . . . . 90 1.12 Pricing formulas of the Black-Scholes type . . . . . . . . . . . . . . 96 1.13 Partial Differential Equations for Pricing Functions and Kernels . . . 108 1.14 American Options . . . . . . . . . . . . . . . . . . . . 114 1.14.1 Arbitrage-Free Pricing and Optimal Stopping Time Formulation 114 1.14.2 Perpetual American Options . . . . . . . . . . . . . . . . . . 125 1.14.3 Properties of the Early-Exercise Boundary . . . . . . . . . . . 127 1.14.4 The PDE and Integral Equation Formulation . . . . . . . . . 129 2 Fixed Income Instruments 135 2.1 Bonds, Futures, Forwards and Swaps . . . . . . . . . . . . . . . . . . 135 2.1.1 Bonds . . . . . . . . . . . . . . . . . . . . . 135 2.1.2 Forward rate agreements . . . . . . . . . . . . . . . . . . . 138 2.1.3 Floating rate notes . . . . . . . . . . . . . . . . . . .

Details

No. of pages:
426
Language:
English
Copyright:
© 2005
Published:
Imprint:
Academic Press
Print ISBN:
9780120476824
Electronic ISBN:
9780080488097

About the editors

Claudio Albanese

Affiliations and Expertise

Professor of Mathematical Finance, Imperial College, London, UK

Giuseppe Campolieti

Affiliations and Expertise

Associate Professor of Mathematics, SHARCNET Chair in Financial Mathematics, Wilfrid Laurier University, Waterloo, Ontario, Canada

Reviews

“Albanese and Campolieti carefully select the most important and relevant topics in financial derivatives pricing and risk management. Their work strikes a fine balance between theory and financial practice. A dozen carefully designed numerical projects are included that serve to introduce students to actual implementation issues in pricing and risk management. The book is succinctly written, with clear and insightful descriptions of state-of-the-art financial models. The style of presentation demonstrates the authors' unique pedagogical exposition of the quantitative and financial concepts in derivative pricing and risk management. Advanced Derivatives Pricing and Risk Management is destined to be a valuable text and reference for students and practitioners in the field of financial engineering.” — Yue Kuen Kwok, Associate Professor, Department of Mathematics, Hong Kong University of Science and Technology “The set of projects on the accompanying CDROM give students and professors the opportunity to work in a simulated environment and can be used, as is the goal here, to train students in building software modules for pricing, hedging, etc. The projects enhance the understanding of the material and extend the book's usefulness by enabling students to tackle other situations not explicitly addressed in the modules provided. VBA is easy to learn and can facilitate rapid developments of real applications. In addition, the choice of Excel as the Graphic User Interface (GUI) is very appropriate. Furthermore, the existence of a built-in visual basic editor allows users to see the code, modify it to suit different needs and to experiment with it. Hence these features facilitate student learning to produce software themselves.” — Eliezer Prisman, Nigel Martin Chair in Finance, Director of the Financial Engineering Collaborative Diploma, Schulich School of Business, York University, Toronto