• In-depth analysis of probability theory and stochastic calculus as well as alternative approaches for products that cannot be valued within these frameworks

• Provides a practical approach for hedging equity products beyond delta hedging and discusses in detail practical software implementation issues

CONTENTS

Introduction

Mathematical Fundamentals

A Review of Probability Theory and Stochastic Calculus
The Black-Scholes Equity Model
Extensions to Black-Scholes
The Clark Formula
The Hybrid Model
The Multi-Currency Hybrid Model

Closed-Form Solutions for Standard Products

Basic Products
American Options
Digital Options
Barrier Options
Asian Options

Closed-Form Solutions for Non-Standard Products

Lookback Options
Fade-In Options
Fade-In Barrier Options
Chooser Options
Prolongation Options
Improving Options
Power and Powered Options
Compound Options
Closed-Form Solutions for Multi-Asset Products
Exchange Options
Relative Digital Options
Relative Outperformance Options
Outperformance options
European Digital Option on Best or Worst of Two Assets
Best or Worst of Several Assets
Basket Options
Hindsight Options
Outside Barrier Options
Outside Digital Options
Closed-Form Fixed Income and Hybrid Products
Bond Options and Swaptions
Caps and Floors
European Options (Merton Formula)
Equity/Bond Outperformance Options

The Tree Approach

Setting up the Tree
Option Pricing Using Trees
Barrier Options
Bermudan Asian Options
Convertible Bonds
Monte Carlo Methods
The Basic Method
Speeding Up Monte Carlo
Generic Monte Carlo Pricing
Hybrid Monte Carlo
Monte Carlo for American Options
A Partial Differential Equation Solver
Discretisation of the PDE
Boundary Conditions
Moving Barriers
Range and Fade-In Options
American Options
Discrete Dividends
Model Calibration
Further Modelling Issues
Calibration of the Extended Vasicek Model
Basket and Asian Underlyings
Volatility Smile

Hedging

Hedging and Risk Management
Pricing and Hedging European Options Under Transaction Costs
Hedging of Specific Products

Implementation Issues

The Context of a Model Library
Library Interface Design
Internal design

Appendix: Useful Formulas
Bibliography

Reviewed by Glyn Holton, Contingency Analysis

This is an extraordinarily good book on equity option pricing. Written by a team of six Deutsche Bank financial engineers, it is targeted specifically toward financial engineers in the equity markets. It is highly practical and mathematically sophisticated. The core of the book is its explanations of how to price a wide variety of OTC equity derivatives, including exotics and derivatives that combine an equity component with either a fixed income or foreign exchange component. However, the book is far more than this. It opens with a sophisticated discussion of the financial mathematics that underlies financial engineering. Depending upon the readers own knowledge, this can be used in either one of two ways. For readers who are familiar with measure-theoretic probability and stochastic calculus, it is a handy reference detailing important definitions and theorems. For less knowledgeable readers, it is an excellent road map for studying such advanced material. It clearly lays out important concepts, motivating what you need to learn if you read such standard texts as Baxter and Rennie, Breiman or Oksendal. Next, there are four chapters detailing closed form solutions for pricing everything from vanilla instruments to multi-asset and hybrid products. Three chapters cover quantitative methods based upon trees, Monte Carlo simulation and differential equations respectively. Other chapters cover volatility smiles, hedging, transaction costs and the development of pricing libraries.

Anyone who is or wants to be a financial engineer in the equity markets needs to read this book. The mathematical discussions are sophisticated, but they are also extremely practical and insightful. For example, the explanation of how to construct Sobol numbers is the best I have ever read. Also, market conventions and other useful information is provided as needed.