Analytical and Numerical Methods for Pricing Financial Derivatives.

✍ Scribed by Mikula, Karol; Sevcovic, Daniel; Stehlikova, Beata

• Publisher: Nova Science Publishers, Inc.
• Year: 2012
• Tongue: English
• Leaves: 327
• Series: Mathematics research developments series.
• Category: Library

✦ Table of Contents

ANALYTICAL AND NUMERICAL METHODS FOR PRICING FINANCIAL DERIVATIVES
ANALYTICAL AND NUMERICAL METHODS FOR PRICING FINANCIAL DERIVATIVES
Library of Congress Cataloging-in-Publication Data
Contents
Preface
Introduction
Chapter 1: The Role of Protecting Financial Portfolios
1.1. Stochastic Character of Financial Assets
1.2. Using Derivative Securities as a Tool for Protecting Volatile Stock Portfolios
1.2.1. Forwards and Futures
1.2.2. Plain Vanilla Call and Put Options
Chapter 2: Black-Scholes and Merton Model
2.1. Stochastic Processes and Stochastic Differential Calculus. 2.1.1. Wiener Process and Geometric Brownian MotionDefinition 2.1.
Definition 2.2.
2.1.2. Itō's Integral and Isometry
Lemma 2.1.
2.1.3. Itō's Lemma for Scalar Random Processes
Lemma 2.2
2.1.4. Itō's Lemma for Vector Random Processes
2.2. The Black-Scholes Equation
2.2.1. A Stochastic Differential Equation for the Option Price
2.2.2. Self-financing Portfolio Management with Zero Growth of Investment
2.3. Terminal Conditions
2.3.1. Pay-off Diagrams for Call and Put Options
2.3.2. Pay-off Diagrams for Combined Option Strategies
2.4. Boundary Conditions for Derivative Prices. 2.4.1. Boundary Conditions for Call and Put Options2.4.2. Boundary Conditions for Combined Option Strategies
Problem Section and Exercises
Chapter 3: European Style of Options
3.1. Pricing Plain Vanilla Call and Put Options
3.2. Pricing Put Options Using Call Option Prices and Forwards, Put-Call Parity
3.3. Pricing Combined Options Strategies: Spreads, Straddles, Condors, Butterflies and Digital Options
3.4. Comparison of Theoretical Pricing Results to Real Market Data
3.5. Black-Scholes Equation for Pricing Index Options
Problem Section and Exercises. Chapter 4: Analysis of Dependence of Option Prices on Model Parameters4.1. Historical Volatility of Stocks
4.1.1. A Useful Identity for Black-Scholes Option Prices
4.2. Implied Volatility
Theorem 4.1.
4.3. Volatility Smile
4.4. Delta of an Option
4.5. Gamma of an Option
4.6. Other Sensitivity Factors: Theta, Vega, Rho
4.6.1. Sensitivity with Respect to a Change in the Interest Rate --
Factor Rho
4.6.2. Sensitivity to the Time to Expiration --
Factor Theta
4.6.3. Sensitivity to a Change in Volatility --
Factor Vega
Problem Section and Exercises. Chapter 5: Option Pricing under Transaction Costs5.1. Leland Model, Hoggard, Wilmott and Whalley Model
5.2. Modeling Option Bid-Ask Spreads by Using Leland's Model
Problem Section and Exercises
Chapter 6: Modeling and Pricing Exotic Financial Derivatives
6.1. Asian Options
6.1.1. A Partial Differential Equation for Pricing Asian Options
6.1.2. Dimension Reduction Method and Numerical Approximation of a Solution
6.2. Barrier Options
6.2.1. Numerical and Analytical Solutions to the Partial Differential Equation for Pricing Barrier Options
6.3. Binary Options
6.4. Compound Options.

✦ Subjects

Options (Finance) -- Prices -- Mathematical models