Mathematics for Finance: An Introduction to Financial Engineering

Mathematics for Finance: An Introduction to Financial Engineering Description

This textbook provides the foundational material for a first-year mathematics course in mathematical finance. The information is provided in a rigorous and comprehensive mathematical manner, assuming only a fundamental understanding of probability and calculus.

The time value of money is covered in the book along with many other important topics, such as the time structure of interest rates, bond, and stock valuation, derivative securities (futures, options), discrete-time modeling, pricing, and hedging. This book is perfect for independent study because it contains a ton of examples, problems, and exercises.

Here’s what you will learn in this course:

Introduction: A Simple Market Model

Basic Notions and Assumptions.

• 2 No-Arbitrage Principle
• 3 One-Step Binomial Model.
• 4 Risk and Return.
• 5 Forward Contracts.
• 6 Call and Put Options
• 7 Managing Risk with Options

Risk-Free Assets

• 1 Time Value of Money
• 1.1 Simple Interest
• 1.2 Periodic Compounding
• 1.3 Streams of Payments
• 1.4 Continuous Compounding.
• 1.5 How to Compare Compounding Methods
• 2 Money Market
• 2.1 Zero-Coupon Bonds
• 2.2 Coupon Bonds
• 2.3 Money Market Account.

Risky Assets 

• 1 Dynamics of Stock Prices
• 1.1 Return
• 1.2 Expected Return
• 2 Binomial Tree Model
• 2.1 Risk-Neutral Probability
• 2.2 Martingale Property
• 3 Other Models
• 3.1 Trinomial Tree Model
• 3.2 Continuous-Time Limit

Discrete Time Market Models

• 1 Stock and Money Market Models
• 1.1 Investment Strategies
• 1.2 The Principle of No Arbitrage
• 1.3 Application to the Binomial Tree Model
• 1.4 Fundamental Theorem of Asset Pricing
• 2 Extended Models

Portfolio Management

• 1 Risk
• 2 Two Securities
• 2.1 Risk and Expected Return on a Portfolio
• 3 Several Securities.
• 3.1 Risk and Expected Return on a Portfolio
• 3.2 Efficient Frontier.
• 4 Capital Asset Pricing Model
• 4.1 Capital Market Line
• 4.2 Beta Factor
• 4.3 Security Market Line

Forward and Futures Contracts

• 1 Forward Contracts
• 1.1 Forward Price
• 1.2 Value of a Forward Contract
• 2 Futures
• 2.1 Pricing
• 2.2 Hedging with Futures

Options: General Properties

• 1 Definitions.
• 2 Put-Call Parity
• 3 Bounds on Option Prices
• 3.1 European Options
• 3.2 European and American Calls on Non-Dividend Paying Stock
• 3.3 American Options
• 4 Variables Determining Option Prices
• 4.1 European Options
• 4.2 American Options
• 5 Time Value of Options

Option Pricing

• 1 European Options in the Binomial Tree Model
• 1.1 One Step
• 1.2 Two Steps
• 1.3 General N-Step Model
• 1.4 Cox–Ross–Rubinstein Formula
• 2 American Options in the Binomial Tree Model
• 3 Black–Scholes Formula

Financial Engineering

• 1 Hedging Option Positions
• 1.1 Delta Hedging
• 1.2 Greek Parameters
• 1.3 Applications
• 2 Hedging Business Risk
• 2.1 Value at Risk
• 2.2 Case Study
• 3 Speculating with Derivatives
• 3.1 Tools
• 3.2 Case Study

Variable Interest Rates

• 1 Maturity-Independent Yields
• 1.1 Investment in Single Bonds
• 1.2 Duration
• 1.3 Portfolios of Bonds
• 1.4 Dynamic Hedging
• 2 General Term Structure
• 2.1 Forward Rates
• 2.2 Money Market Account

Stochastic Interest Rates

• 1 Binomial Tree Model
• 2 Arbitrage Pricing of Bonds
• 2.1 Risk-Neutral Probabilities
• 3 Interest Rate Derivative Securities
• 3.1 Options
• 3.2 Swaps
• 3.3 Caps and Floors
• 4 Final Remarks

Solutions

Bibliography

Glossary of Symbols

Index