Equity Derivatives

Theory and Applications

Marcus Overhaus, Andrew Ferraris, Thomas Knudsen, Frank Mao, Laurent Nguyen-Ngoc, Gero Schindlmayr

• Publisher: Wiley
• Year: 2011
• Print ISBN: 9780471436461
• eBook ISBN: 9781118160879
• Edition: 1
• Topic: Business
• Subtopic: Finanza
• Index: Business

Written by the quantitative research team of Deutsche Bank, the world leader in innovative equity derivative transactions, this book acquaints readers with leading-edge thinking in modeling and hedging these transactions. Equity Derivatives offers a balanced, integrated presentation of theory and practice in equity derivative markets. It provides a theoretical treatment of each new modeling and hedging concept first, and then demonstrates their practical application. The book covers: the newest and fastest-growing class of derivative instruments, fund derivatives; cutting-edge developments in equity derivative modeling; new developments in correlation modeling and understanding volatility skews; and new Web-based implementation/delivery methods.
Marcus Overhaus, PhD, Andrew Ferraris, DPhil, Thomas Knudsen, PhD, Frank Mao, PhD, Ross Milward, Laurent Nguyen-Ngoc, PhD, and Gero Schindlmayr, PhD, are members of the Quantitative Research team of Deutsche Bank's Global Equity Division, which is based in London and headed by Dr. Overhaus.

CHAPTER 1

Mathematical Introduction

The use of probability theory and stochastic calculus is now an established standard in the field of financial derivatives. During the last 30 years, a large amount of material has been published, in the form of books or papers, on both the theory of stochastic processes and their applications to finance problems. The goal of this chapter is to introduce notions on probability theory and stochastic calculus that are used in the applications presented afterwards. The notations used here will remain identical throughout the book.

We hope that the reader who is not familiar with the theory of stochastic processes will find here an intuitive presentation, although rigorous enough for our purposes, and a set of useful references about the underlying mathematical theory. The reader acquainted with stochastic calculus will find here an introduction of objects and notations that are used constantly, although maybe not very explicitly.

This chapter does not aim at giving a thorough treatment of the theory of stochastic processes, nor does it give a detailed view of mathematical finance theory in general. It recalls, rather, the main general facts that will be used in the examples developed in the next chapters.

1.1 PROBABILITY BASIS

Financial models used for the evaluation of derivatives are mainly concerned with the uncertainty of the future evolution of the stock prices. The theory of probability and stochastic processes provides a framework with a form of uncertainty, called randomness. A probability space Ω is assumed to be given once and for all, interpreted as consisting of all the possible paths of the prices of securities we are interested in. We will suppose that this probability space is rich enough to carry all the random objects we wish to construct and use. This assumption is not restrictive for our purposes, because we could always enlarge the space Ω, for example, by considering a product space. Note that Ω can be chosen to be a “canonical space,” such as the space of continuous functions, or the space of cadlag (French acr...

Table of contents

• Cover
• Contents
• Title
• Copyright
• About the Authors
• Preface
• Chapter 1: Mathematical Introduction
• Chapter 2: Incomplete Markets
• Chapter 3: Financial Modeling with Lévy Processes
• Chapter 4: Finite-Difference Methods for Multifactor Models
• Chapter 5: Convertible Bonds and Asset Swaps
• Chapter 6: Data Representation
• Chapter 7: Application Connectivity
• Chapter 8: Web-Based Quantitative Services
• Chapter 9: Portfolio and Hedging Simulation
• References
• Index