Problems and Solutions in Mathematical Finance : Commodity and Foreign Exchange Derivatives

Problems and Solutions in Mathematical Finance -- Contents -- Preface -- About the Authors -- 1 Basic Equity Derivatives Theory -- 1.1 Introduction -- Option Trading -- Forward Contract -- Futures Contract -- Stock Split (Divide) Effect -- Stock Dividend Effect -- Hedging Strategies -- 1.2 Problems and Solutions -- 1.2.1 Forward and Futures Contracts -- 1.2.2 Options Theory -- 1.2.3 Hedging Strategies -- 2 European Options -- 2.1 Introduction -- 2.2 Problems and Solutions -- 2.2.1 Basic Properties -- 2.2.2 Black-Scholes Model -- 2.2.3 Tree-Based Methods -- 2.2.4 The Greeks -- 3 American Options -- 3.1 Introduction -- Optimal Stopping Time Formulation -- Free Boundary Formulation -- Linear Complementarity Formulation -- Binomial Option Pricing -- 3.2 Problems and Solutions -- 3.2.1 Basic Properties -- 3.2.2 Time-Independent Options -- 3.2.3 Time-Dependent Options -- 4 Barrier Options -- 4.1 Introduction -- In-Out Parity -- Barrier Options Pricing -- Probabilistic Approach -- Partial Differentiation Equation Approach -- 4.2 Problems and Solutions -- 4.2.1 Probabilistic Approach -- 4.2.2 Reflection Principle Approach -- 4.2.3 Further Barrier-Style Options -- 5 Asian Options -- 5.1 Introduction -- Average Rate (Fixed Strike) Option Payoff -- Average Strike (Floating Strike) Option Payoff -- Put-Call Parity -- 5.2 Problems and Solutions -- 5.2.1 Discrete Sampling -- 5.2.2 Continuous Sampling -- 6 Exotic Options -- 6.1 Introduction -- Path-Independent Options -- Path-Dependent Options -- 6.2 Problems and Solutions -- 6.2.1 Path-Independent Options -- 6.2.2 Path-Dependent Options -- 7 Volatility Models -- 7.1 Introduction -- Historical Volatility -- Implied Volatility -- Local Volatility -- Stochastic Volatility -- 7.2 Problems and Solutions -- 7.2.1 Historical and Implied Volatility -- 7.2.2 Local Volatility -- 7.2.3 Stochastic Volatility