Introduction to Financial Mathematics : With Computer Applications (Hardcover)

Chapter 1. Introduction to Financial Derivatives and Valuation. 1.1. Foundations in Economics and Finance. 1.2. Introduction to the Valuation of Financial Contracts. 1.3. Details Regarding Forward Contracts. 1.4. The Arbitrage-free Pricing of Forward Contracts. 1.5. Introduction to Option Contracts. 1.6. Put-Call Parity and Arbitrage. 1.7. Arbitrage-free Option Pricing. 1.8. Compound Options and Option Strategies. 1.9. The Limits to Arbitrage and Complete Markets. 1.10. Computing System: Mathematica and R. Chapter 2. Introduction to Interest Rates, Bonds and Equities. 2.1. The Time Value of Money and Interest Rates. 2.2. Term Structures, Yield Curves, and Forward Rates. 2.3. Fixed Income Risk Measurement and Management. 2.4. Equities and Equity Valuation. 2.5. Asset Pricing and Equity Risk Management. Chapter 3. Fundamentals of Financial Derivative Pricing. 3.1. Overview of the Three Primary Derivative Pricing Approaches. 3.2. The Binomial Tree Model Approach to Derivative Pricing. 3.3. The Geometric Brownian Motion and Monte-Carlo Simulation. 3.4. Analytical Model Approaches to Derivative Pricing. Chapter 4. More About Derivative Pricing. 4.1. Various Methods to Value Derivatives. 4.2. Various Exotic Derivatives. 4.3. Dividends. 4.4. More on Forward Values, Futures Contracts, and Futures Prices. Chapter 5. Risk Management and Hedging Strategies. 5.1. Simple Hedging Using Forward and Futures Contracts. 5.2. One-to-h Hedging Using Forward and Futures Contracts. 5.3. Delta Hedging of Options Portfolio Using Underlying Asset. 5.4. Delta Hedging Using Futures. 5.5. Greek Letter Hedging of Other Option Risk Factors. 5.6. Duration Hedging of Fixed Income Instruments and Interest Rate Risk. 5.7. Hedging Various Risks Using Swap Contracts. Chapter 6. Portfolio Management. 6.1. Markowitz Frontier. 6.2. Portfolio Optimization: Linear and Quadratic Programming. 6.3. The Optimal Growth Portfolio. Chapter 7. Interest Rate Derivatives Modeling and Risk Management in the HJM Framework. 7.1. Zero Coupon Bonds, Forward rates, Short Rates and Money Markets in a Deterministic World. 7.2. Risk neutral Valuation in a One Factor HJM Model. 7.3. Valuation and Risk Management of Options on Bonds and in a One Factor HJM. 7.4. Valuation and Risk Management of Caps, Floors, and Interest Rate Swaps in a One Factor HJM Model. 7.5. Pricing and Risk Management of Forward and Futures Contracts on a Bond in a One Factor HJM Model. 7.6. Calibrating the HJM Model Parameters from the Market Prices. Chapter 8. Credit Risk and Credit Derivatives. 8.1. Default Probabilities and Extract Default Probabilities from Market. 8.2. Single-Name Credit Derivatives. 8.3. Collateralized Debt Obligations (CDOs) and CDO Model with Independent Bond Defaults. 8.4. Collateralized Debt Obligations (CDOs) Model with Positively Correlated Bond Defaults. 8.5. CDO Squared. 8.6. The Financial Crisis and Credit Derivatives