Quantitative finance: a simulation-based introduction using excel

Table of Contents
Introduction

Intuition about Uncertainty and Risk
Introduction
Individual Attitudes toward Risk
The St. Petersburg Paradox
Looking Forward to Chapter 3

The Classical Approach to Decision Making under Uncertainty
Map to the Future

Valuing Investment Opportunities: The Discounted Cash Flow Method
Discounted Cash Flow Method for Evaluating Investment Opportunities
Conclusions

Repaying Loans Over Time
Introduction
Repaying a Loan over Time: Excel
Repaying a Loan over Time: Mathematics
First-Order Difference Equations
Solving the Loan Repayment Difference Equation
More Examples of Using Difference Equations to Find Loan Payments
Writing the Difference Equation in Forward versus Backward Forms
Bridges to the Future

Bond Pricing with Default: Using Simulations
Modeling a Defaultable Bond or Loan
Financial Insights
Simulating Loan Portfolios
What Happens if There Are a Large Number of Independent Loans?
Bridge to the Future

Bond Pricing with Default: Using Difference Equations
Risky Bonds
Using Difference Equations to Find C
Exploring the Insights Arising from Equation 7.5
Determining Recovery Rates
Determining the Probability of Default
A Bridge to the Future

Difference Equations for Life Annuities
Introduction

Tranching and Collateralized Debt Obligations
Collateralized Debt Obligations
Tranched Portfolios
The Detailed Calculation
Correlation of Two Identical Bonds
Conclusion

Bond CDOs: More Than Two Bonds, Correlation, and Simulation
Introduction
Using an Excel Simulation to Analyze CDOs with More Than Two Bonds
Collateralized Debt Obligations: An Example of Financial Engineering
The Binomial Simplification
Correlated Defaults

Fundamentals of Fixed Income Markets
What Are Bonds?
Getting Down to Quantitative Details
Simplest Bond Pricing Equation
How Bonds Are Traded in Canada
Clean and Dirty Bond Prices
Conclusion and Bridge to the Next

Yield Curves and Bond Risk Measures
Introduction
Constructing Yield Curves from Bond Prices
Bond Price Sensitivities to the Yield

Forward Rates
Introduction
Relationships between Forward Rates and the Yield Curve
Yield Curves, Discount Factors, and Forward Rates
Interpreting Forward Curves

Modeling Stock Prices
What Are Stocks?
Simple Statistical Analysis of Real Stock Data

Mean Variance Portfolio Optimization
Selecting Portfolios
CAPM and Markowitz

A Qualitative Introduction to Options
Stock Option Definitions
Uses for Put and Call Options
Qualitative Behavior of Puts and Calls

Value at Risk (VaR)
Introduction to Value at Risk
Pitfalls of VaR
Summary

Pricing Options Using Binomial Trees
Introduction
Binomia l Model
Single-Period Binomial Tree Model for Option Pricing
Extending the Binomial Model to Multiple Time Steps
Multiple-Step Binomial Trees
Summary

Random Walks
Introduction
Deriving the Diffusion Partial Differential Equation

Basic Stochastic Calculus
Basics of Stochastic Calculus
Stochastic Integration by Examples
Conclusions and Bridge to Next Chapters

Simulating Geometric Brownian Motion
Simulating GBM Stock Prices at a Single Future Time
Simulating a Time Sequence of GBM Stock Prices
Summary

Black Scholes PDE for Pricing Options in Continuous Time
Introduction
Hedging Argument
Call Price Solution of the Black Scholes Equation
Why Short Selling Is So Dangerous
Summary and Bridge to the Future

Solving the Black Scholes PDE
Solving the Black Scholes Partial PDE for a European Call
General European Option Payoffs: Risk-Neutral Pricing
Summary

Pricing Put Options Using Put Call Parity
Summary

Some Approximate Values of the Black Scholes Call Formula
Approximate Call Formulas at-the-Money
Approximate Call Values Near-the-Money
Approximate Call Values Far-from-the-Money

Simulating Delta Hedging
Introduction
How Does Delta Hedging Really Work?
Understanding the Results of the Delta Hedging Process
The Impact of Transaction Costs
A Hedgers Perspective on Option Gamma or, "Big Gamma" = "Big Money"
Bridge to the Future

Black Scholes with Dividends
Modeling Dividends
The Black Scholes PDE for the Continuously Paid Dividend Case
Pricing the Prepaid Forward on a Continuous Dividend Paying Stock
More Complicated Derivatives on Underlying Paying Continuous Dividends

American Options
Introduction and Binomial Pricing
American Puts
American Calls

Pricing the Perpetual American Put and Call
Perpetual Options: Underlying Pays No Dividends
Basic Perpetual American Call
Perpetual American Call/Put Model with Dividends
The Perpetual American Call, Continuous Dividends

Options on Multiple Underlying Assets
Exchange Options

Interest Rate Models
Setting the Stage for Stochastic Interest Rate Models
Pricing When You CANNOT Trade the Underlying Asset
Hedging Bonds in Continuous Time
Solving the Bond Pricing PDE
Vasicek Model
Summary

Incomplete Markets
Introduction to Incomplete Markets
Trying to Hedge Options on a Trinomial Tree
Minimum Variance Hedging of a European Option with Default
Binomial Tree Model with Default Risk

Appendix 1: Probability Theory Basics—Experiments, Sample Outcomes, Events, and Sample Space
Appendix 2: Proof of De Moivre–Laplace Theorem Using MGF
Appendix 3: Naming Variables in Excel
Appendix 4: Building VBA Macros from Excel

Book Description
Teach Your Students How to Become Successful Working Quants

Quantitative Finance: A Simulation-Based Introduction Using Excel provides an introduction to financial mathematics for students in applied mathematics, financial engineering, actuarial science, and business administration. The text not only enables students to practice with the basic techniques of financial mathematics, but it also helps them gain significant intuition about what the techniques mean, how they work, and what happens when they stop working.

After introducing risk, return, decision making under uncertainty, and traditional discounted cash flow project analysis, the book covers mortgages, bonds, and annuities using a blend of Excel simulation and difference equation or algebraic formalism. It then looks at how interest rate markets work and how to model bond prices before addressing mean variance portfolio optimization, the capital asset pricing model, options, and value at risk (VaR). The author next focuses on binomial model tools for pricing options and the analysis of discrete random walks. He also introduces stochastic calculus in a nonrigorous way and explains how to simulate geometric Brownian motion. The text proceeds to thoroughly discuss options pricing, mostly in continuous time. It concludes with chapters on stochastic models of the yield curve and incomplete markets using simple discrete models.

Accessible to students with a relatively modest level of mathematical background, this book will guide your students in becoming successful quants. It uses both hand calculations and Excel spreadsheets to analyze plenty of examples from simple bond portfolios. The spreadsheets are available on the book’s CRC Press web page.