Introducing Financial Mathematics: Theory, Binomial Models, and Applications (Chapman and Hall/CRC Financial Mathematics Series)

Cover
Half Title
Series Page
Title Page
Copyright Page
Dedication
Contents
Preface
1. Basics
	1.1. Assets and Portfolios
		1.1.1. Stocks and Bonds
		1.1.2. Foreign Exchange
		1.1.3. Derivatives
		1.1.4. Riskless Return
		1.1.5. Interest Rates and Present Value
	1.2. Payoff and Profit Graphs
		1.2.1. Payoff Graphs for Forward Contracts
		1.2.2. Payoff and Profit Graphs for Options
		1.2.3. Payoff and Profit Graphs for Contingent Options
	1.3. Arbitrage
		1.3.1. Random Variables and Stochastic Processes
		1.3.2. Deterministic Arbitrages
		1.3.3. Arbitrage and Expected Value
	1.4. No Arbitrage and Its Consequences
		1.4.1. Hedging
		1.4.2. Martingales and Fair Prices
		1.4.3. No-Arbitrage Price Equalities
		1.4.4. No-Arbitrage Inequalities
	1.5. Exercises
	1.6. Further Reading
2. Continuous Models
	2.1. Some Facts from Probability Theory
	2.2. Understanding Brownian Motion
	2.3. The Black-Scholes Formula
		2.3.1. Option Pricing
		2.3.2. Historical Note
		2.3.3. Black-Scholes Greeks
	2.4. Implementation
		2.4.1. Numerical Differentiation
		2.4.2. Interpolation
		2.4.3. Regression
	2.5. Exercises
	2.6. Further Reading
3. Discrete Models
	3.1. One-Step, Two-State Models
		3.1.1. Risk Neutral Probabilities
		3.1.2. Pricing Derivatives by Hedging
		3.1.3. Pricing Foreign Exchange Derivatives by Hedging
		3.1.4. Zero-Coupon Bonds of Different Maturity
	3.2. One-Step, Multistate Models
	3.3. Multistep Binomial Models
		3.3.1. Recombining Models
		3.3.2. Generalized Backward Induction Pricing
		3.3.3. Arrow-Debreu Securities
		3.3.4. Jamshidian’s Forward Induction Formula
		3.3.5. Zero-Coupon Bonds and Interest Rate Constraints
	3.4. The Cox-Ross-Rubinstein Model
		3.4.1. Arrow-Debreu Decomposition in CRR
		3.4.2. Limit of CRR as N → ∞
		3.4.3. CRR Greeks
	3.5. Exercises
	3.6. Further Reading
4. Exotic Options
	4.1. Recombining Binomial Tree Prices
		4.1.1. European-Style Options in CRR
		4.1.2. American-Style Options in CRR
		4.1.3. Binary Options in CRR
		4.1.4. Compound Options in CRR
		4.1.5. Chooser Options in CRR
		4.1.6. Forward Start Options in CRR
		4.1.7. Barrier Options
		4.1.8. Booster Options
	4.2. Path Dependent Prices
		4.2.1. Efficient Data Structures
		4.2.2. Paths in Recombining Trees
		4.2.3. Path Dependent Arrow-Debreu Securities
		4.2.4. Asian-Style Options
		4.2.5. Floating Strike Options
		4.2.6. Lookback Options
		4.2.7. Ladder Options
	4.3. Exercises
	4.4. Further Reading
5. Forwards and Futures
	5.1. Discrete Models for Forwards
		5.1.1. No-Arbitrage Forwards Values
		5.1.2. Binomial Models for Forwards Prices
	5.2. Discrete Models for Futures
		5.2.1. Binomial Models for Futures Prices
		5.2.2. No-Arbitrage Futures Values
		5.2.3. Margin Calls and Defaults
	5.3. Exercises
	5.4. Further Reading
6. Dividends and Interest
	6.1. Stocks with Dividends
		6.1.1. Effects on Forwards
		6.1.2. Effects on American Call Options
		6.1.3. Dividends as Cash Flows
	6.2. Interest Rates
		6.2.1. Zero-Coupon Bonds
		6.2.2. Coupon Bonds
		6.2.3. Cash Flow Swaps
		6.2.4. Benchmarks
	6.3. Exercises
	6.4. Further Reading
7. Implied Volatility
	7.1. The Inverse Problem for Volatility
	7.2. Implied Volatility Surfaces
	7.3. Implied Binomial Trees
		7.3.1. Path Independent Probabilities
		7.3.2. Jackwerth’s Generalization
		7.3.3. Rubinstein’s One-Two-Three Algorithm
	7.4. Exercises
	7.5. Further Reading
8. Fundamental Theorems
	8.1. Finite Financial Models
		8.1.1. Arbitrage and Positivity
		8.1.2. Fundamental Theorems of Asset Pricing
	8.2. Applications of the Fundamental Theorems
		8.2.1. Hedges
		8.2.2. Complete Markets
		8.2.3. Incomplete Markets
	8.3. Cones, Convexity, and Duals
		8.3.1. Open and Closed Sets
		8.3.2. Dual Cones and Double Duals
		8.3.3. Proofs of the Fundamental Theorems
		8.3.4. Farkas’s Lemma
		8.3.5. Hyperplane Separation
	8.4. Exercises
	8.5. Further Reading
9. Project Suggestions
A. Answers
	A.1. . . . to Chapter 1 Exercises
	A.2. . . . to Chapter 2 Exercises
	A.3. . . . to Chapter 3 Exercises
	A.4. . . . to Chapter 4 Exercises
	A.5. . . . to Chapter 5 Exercises
	A.6. . . . to Chapter 6 Exercises
	A.7. . . . to Chapter 7 Exercises
	A.8. . . . to Chapter 8 Exercises
Index