Equity derivatives are a continuing success story that offer more flexibility and hedging opportunities than ever before. They comprise one of the most important components of capital markets. For this reason, it is imperative that financial professionals–from risk managers to derivatives traders–understand how equity derivatives are priced, hedged, utilized, and implemented via new technologies.

Written by the quantitative research team of Deutsche Bank, the world leader in equity derivative transactions, Equity Derivatives: Theory and Applications is the definitive reference on the advanced use of these financial instruments. Pushing into new and cutting-edge areas of modeling and hedging, this book provides a balanced, integrated presentation of theory and practice. The theoretical treatment of each new modeling and hedging concept is followed by a demonstration of its practical application. Developments in areas such as equity-linked structures and volatility modeling, and the delivery of pricing over the Internet, are clearly analyzed and presented, using graphs, formulas, and examples that are truly unique to this book.

Each chapter highlights important facets of equity derivatives, including:
a. An introduction of probability theory and stochastic calculus that
provides the mathematical foundation needed to understand the
examples presented
b. Pricing and hedging in incomplete markets
c. A thorough explanation of Lévy processes and their application to
finance, e.g., extended Heston model
d. Two-factor finite difference techniques
e. In-depth analysis of convertible bonds and the advantages of
convertible bond asset swaps

Equity Derivatives: Theory and Applications also covers recent developments and new technologies that are fostering the delivery of pricing and hedging analytics over the Internet and company intranets–from outlining XML, the emerging standard for representing and transmitting various types of data, to the technologies available for distributed computing, namely SOAP and Web services. Not only will you come to learn how systems can be configured to represent financial market data in the context of equity derivatives, you will actually see how these applications function in the real world through vivid examples and illustrations.

TABLE OF CONTENTS

Chapter 1 Mathematical Introduction
1.1 Probability Basis
1.2 Processes
1.3 Stochastic Calculus
1.4 Financial Interpretations
1.5 Two Canonical Examples

Chapter 2 Incomplete Markets
2.1 Martingale Measures
2.2 Self-Financing Strategies, Completeness, and No Arbitrage
2.3 Examples
2.4 Martingale Measures, Completeness, and No Arbitrage
2.5 Completing the Market
2.6 Pricing in Incomplete Markets
2.7 Variance-Optimal Pricing and Hedging
2.8 Super Hedging and Quantile Hedging

Chapter 3 Financial Modeling with Levy Processes
3.1 A Primer on Levy Processes
3.2 Modeling with Levy Processes
3.3 Products and Models
3.4 Model Calibration and Smile Replication
3.5 Numerical Methods for Levy Processes
3.6 A Model Involving Levy Processes

Chapter 4 Finite-Difference Methods for Multifactor Models
4.1 Pricing Models and PDEs
4.2 The Pricing PDE and Its Discretization
4.3 Explicit and Implicit SchemeS
4.4 The ADI Scheme
4.5 Convergence and Performance
4.6 Dividend Treatment in Stochastic Volatility Models

Chapter 5 Convertible Bonds and Asset Swaps
5.1 Convertible Bonds
5.2 Convertible Bond Asset Swaps

Chapter 6 Data Representation
6.1 XML
6.2 XML Schema
6.3 XML Transformation
6.4 Representing Equity Derivative Market Data

Chapter 7 Application Connectivity
7.1 Components
7.2 Distributed Components
7.3 SOAP
7.4 Web Services

Chapter 8 Web-Based Quantitative Services
8.1 Web Pricing Servers
8.2 Model Integration into Risk Management and Booking Systems
8.3 Web Applications and Dynamic Web Pages

Chapter 9 Portfolio and Hedging Simulation
9.1 Introduction
9.2 Algorithm and Software Design
9.3 Example: Discrete Hedging and Volatility Misspecification
9.4 Example: Hedging a Heston Market
9.5 Example: Constant Proportion Portfolio Insurance
9.6 Server Integration

References
Index