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## Book Description

In an easy-to-understand, nontechnical yet mathematically elegant manner, An Introduction to Exotic Option Pricing shows how to price exotic options, including complex ones, without performing complicated integrations or formally solving partial differential equations (PDEs). The author incorporates much of his own unpublished work, including ideas and techniques new to the general quantitative finance community.

The first part of the text presents the necessary financial, mathematical, and statistical background, covering both standard and specialized topics. Using no-arbitrage concepts, the Black–Scholes model, and the fundamental theorem of asset pricing, the author develops such specialized methods as the principle of static replication, the Gaussian shift theorem, and the method of images. A key feature is the application of the Gaussian shift theorem and its multivariate extension to price exotic options without needing a single integration.

The second part focuses on applications to exotic option pricing, including dual-expiry, multi-asset rainbow, barrier, lookback, and Asian options. Pushing Black–Scholes option pricing to its limits, the author introduces a powerful formula for pricing a class of multi-asset, multiperiod derivatives. He gives full details of the calculations involved in pricing all of the exotic options.

Taking an applied mathematics approach, this book illustrates how to use straightforward techniques to price a wide range of exotic options within the Black–Scholes framework. These methods can even be used as control variates in a Monte Carlo simulation of a stochastic volatility model.

1. Preliminaries
2. Symbols and Abbreviations
3. Preface
4. Part I Technical Background
1. Chapter 1 Financial Prelinaries
1. 1.1 European Derivative Securities
2. 1.2 Exotic Options
3. 1.3 Binary Options
4. 1.4 No-Arbitrage
5. 1.5 Pricing Methods
6. 1.6 The Black-Scholes PDE Method
7. 1.7 Derivation of Black-Scholes PDE
8. 1.8 Meaning of the Black-Scholes PDE
9. 1.9 The Fundamental Theorem of Asset Pricing
10. 1.10 The EMM Pricing Method
11. 1.11 Black-Scholes and the FTAP
12. 1.12 Effect of Dividends
13. 1.13 Summary
14. Exercise Problems
2. Chapter 2 Mathematical Preliminaries
1. 2.1 Probability Spaces
2. 2.2 Brownian Motion
3. 2.3 Stochastic DE’s
4. 2.4 Stochastic Integrals
5. 2.5 Ito’s Lemma
6. 2.6 Martingales
7. 2.7 Feynman-Kac Formula
8. 2.8 Girsanov’s Theorem
9. 2.9 Time Varying Parameters
10. 2.10 The Black-Scholes PDE
11. 2.11 The BS Green’s Function
12. 2.12 Log-Volutions
13. 2.13 Summary
14. Exercise Problems
3. Chapter 3 Gaussian Random Variables
1. 3.1 Univariate Gaussian Random Variables
2. 3.2 Gaussian Shift Theorem
3. 3.3 Rescaled Gaussians
4. 3.4 Gaussian Moments
5. 3.5 Central Limit Theorem
6. 3.6 Log-Normal Distribution
7. 3.7 Bivariate Normal
8. 3.8 Multi-Variate Gaussian Statistics
9. 3.9 Multi-Variate Gaussian Shift Theorem
10. 3.10 Multi-Variate Ito’s Lemma and BS-PDE
11. 3.11 Linear Transformations of Gaussian RVs
12. 3.12 Summary
13. Exercise Problems
5. Part II Applications to Exotic Option Pricing
1. Chapter 4 Simple Exotic Options
2. Chapter 5 Dual Expiry Options
1. 5.1 Forward Start Calls and Puts
2. 5.2 Second-Order Binaries
3. 5.3 Second-Order Asset and Bond Binaries
4. 5.4 Second-Order Q-Options
5. 5.5 Compound Options
6. 5.6 Chooser Options
7. 5.7 Reset Options
8. 5.8 Simple Cliquet Option
9. 5.9 Summary
10. Exercise Problems
3. Chapter 6 Two-Asset Rainbow Options
1. 6.1 Two-Asset Binaries
2. 6.2 The Exchange Option
3. 6.3 Options on the Minimum/Maximum of Two Assets
4. 6.4 Product and Quotient Options
5. 6.5 ICIAM Option Competition
6. 6.6 Executive Stock Option
7. 6.7 Summary
8. Exercise Problems
4. Chapter 7 Barrier Options
1. 7.1 Introduction
2. 7.2 Method of Images
3. 7.3 Barrier Parity Relations
4. 7.4 Equivalent Payoffs for Barrier Options
5. 7.5 Call and Put Barrier Options
6. 7.6 Barrier Option Rebates
7. 7.7 Barrier Option Extensions
8. 7.8 Binomial Model for Barrier Options
9. 7.9 Partial Time Barrier Options
10. 7.10 Double Barriers
11. 7.11 Sequential Barrier Options
12. 7.12 Compound Barrier Options
13. 7.13 Outside Barrier Options
14. 7.14 Reflecting Barriers
15. 7.15 Summary
16. Exercise Problems
5. Chapter 8 Lookback Options
6. Chapter 9 Asian Options
1. 9.1 Introduction
2. 9.2 Pricing Framework
3. 9.3 Geometric Mean Asian Options
4. 9.4 FTAP Method for GM Asian Options
5. 9.5 PDE Method for GM Asian Options
6. 9.6 Discrete GM Asian Options
7. 9.7 Summary
8. Exercise Problems
7. Chapter 10 Exotic Multi-Options
8. References