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An Introduction to Exotic Option Pricing

Peter Buchen
Publisher: 
Chapman & Hall/CRC
Publication Date: 
2012
Number of Pages: 
278
Format: 
Hardcover
Series: 
Chapman & Hall/CRC Financial Mathematics Series
Price: 
79.95
ISBN: 
9781420091007
Category: 
Monograph
We do not plan to review this book.

TECHNICAL BACKGROUND
Financial Preliminaries
European Derivative Securities
Exotic Options
Binary Options
No-Arbitrage
Pricing Methods
The Black–Scholes PDE Method
Derivation of Black–Scholes PDE
Meaning of the Black–Scholes PDE
The Fundamental Theorem of Asset Pricing
The EMM Pricing Method
Black–Scholes and the FTAP
Effect of Dividends

Mathematical Preliminaries
Probability Spaces
Brownian Motion
Stochastic Des
Stochastic Integrals
Itô’s Lemma
Martingales
Feynman-Kac Formula
Girsanov’s Theorem
Time Varying Parameters
The Black–Scholes PDE
The BS Green’s Function
Log-Volutions

Gaussian Random Variables
Univariate Gaussian Random Variables
Gaussian Shift Theorem
Rescaled Gaussians
Gaussian Moments
Central Limit Theorem
Log-Normal Distribution
Bivariate Normal
Multivariate Gaussian Statistics
Multivariate Gaussian Shift Theorem
Multivariate Itô’s Lemma and BS-PDE
Linear Transformations of Gaussian RVs

APPLICATIONS TO EXOTIC OPTION PRICING
Simple Exotic Options
First-Order Binaries
BS-Prices for First-Order Asset and Bond Binaries
Parity Relation
European Calls and Puts
Gap and Q-Options
Capped Calls and Puts
Range Forward Contracts
Turbo Binary
The Log-Contract
Pay-at-Expiry and Money-Back Options
Corporate Bonds
Binomial Trees
Options on a Traded Account

Dual Expiry Options
Forward Start Calls and Puts
Second-Order Binaries
Second-Order Asset and Bond Binaries
Second-Order Q-Options
Compound Options
Chooser Options
Reset Options
Simple Cliquet Option

Two-Asset Rainbow Options
Two-Asset Binaries
The Exchange Option
Options on the Minimum/Maximum of Two Assets
Product and Quotient Options
ICIAM Option Competition
Executive Stock Option

Barrier Options
Introduction
Method of Images
Barrier Parity Relations
Equivalent Payoffs for Barrier Options
Call and Put Barrier Options
Barrier Option Rebates
Barrier Option Extensions
Binomial Model for Barrier Options
Partial Time Barrier Options
Double Barriers
Sequential Barrier Options
Compound Barrier Options
Outside-Barrier Options
Reflecting Barriers

Lookback Options
Introduction
Equivalent Payoffs for Lookback Options
The Generic Lookback Options m(x, y, t) and M(x, z, t)
The Standard Lookback Calls and Puts
Partial Price Lookback Options
Partial Time Lookback Options
Extreme Spread Options
Look-Barrier Options

Asian Options
Introduction
Pricing Framework
Geometric Mean Asian Options
FTAP Method for GM Asian Options
PDE Method for GM Asian Options
Discrete GM Asian Options

Exotic Multi-Options
Introduction
Matrix and Vector Notation
The M-Binary Payoff
Valuation of the M-Binary
Previous Results Revisited
Multi-Asset, One-Period Asset and Bond Binaries
Quality Options
Compound Exchange Option
Multi-Asset Barrier Options

References

Index

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