This book is an outgrowth of notes compiled by the author while teaching courses for undergraduate and masters/MBA finance students at Washing-ton University in St. Louis and the Institut ffir HShere Studien in Vienna. At one time, a course in Options and Futures was considered an advanced finance elective, but now such a course is nearly mandatory for any finance major and is an elective chosen by many non-finance majors as well. Moreover, students are exposed to derivative securities in courses on Investments, International Finance, Risk Management, Investment Banking, Fixed Income, etc. This ex-pansion of education in derivative securities mirrors the increased importance of derivative securities in corporate finance and investment management.

Part Ⅰ Introduction to Option Pricing

 1 Asset Pricing Basics

1.1 Fundamental Concepts

1.2 State Prices in a One-Period Binomial Model

1.3 Probabilities and Numeraires

1.4 Asset Pricing with a Continuum of States

1.5 Introduction to Option Pricing

1.6 An Incomplete Markets Example

Problems

 2 Continuous-Time Models

2.1 Simulating a Brownian Motion

2.2 Quadratic Variation

2.3 It6 Processes

2.4 It6's Formula

2.5 Multiple It6 Processes

2.6 Examples of It6's Formula

2.7 Reinvesting Dividends

2.8 Geometric Brownian Motion

2.9 Numeraires and Probabilities

2.10 Tail Probabilities of Geometric Brownian Motions

2.11 Volatilities

Problems

 3 Black-Scholes

3.1 Digital Options

3.2 Share Digitals

3.3 Puts and Calls

3.4 Greeks

3.5 Delta Hedging

3.6 Gamma Hedging

3.7 Implied Volatilities

3.8 Term Structure of Volatility

3.9 Smiles and Smirks

3.10 Calculations in VBA

Problems

 4 Estimating and Modelling Volatility

4.1 Statistics Review

4.2 Estimating a Constant Volatility and Mean

4.3 Estimating a Changing Volatility

4.4 GARCH Models

4.5 Stochastic Volatility Models

4.6 Smiles and Smirks Again

4.7 Hedging and Market Completeness

Problems

 5 Introduction to Monte Carlo and Binomial Models

5.1 Introduction to Monte Carlo

5.2 Introduction to Binomial Models

5.3 Binomial Models for American Options

5.4 Binomial Parameters

5.5 Binomial Greeks

5.6 Monte Carlo Greeks I: Difference Ratios

5.7 Monte Carlo Greeks II: Pathwise Estimates

5.8 Calculations in VBA

Problems

Part Ⅱ Advanced Option Pricing

 6 Foreign Exchange

6.1 Currency Options

6.2 Options on Foreign Assets Struck in Foreign Currency

6.3 Options on Foreign Assets Struck in Domestic Currency

6.4 Currency Forwards and Futures

6.5 Quantos

6.6 Replicating Quantos

6.7 Quanto Forwards

6.8 Quanto Options

6.9 Return Swaps

6.10 Uncovered Interest Parity

Problems

 7 Forward, Futures and Exchange Options

7.1 Margrabe's Formula

7.2 Black's Formula

7.3 Merton's Formula

7.4 Deferred Exchange Options

7.5 Calculations in VBA

7.6 Greeks and Hedging

7.7 The Relation of Futures Prices to Forward Prices

7.8 Futures Options

7.9 Time-Varying Volatility

7.10 Hedging with Forwards and Futures

7.11 Market Completeness

Problems

 8 Exotic Options

8.1 Forward-Start Options

8.2 Compound Options

8.3 American Calls with Discrete Dividends

8.4 Choosers

8.5 Options on the Max or Min

8.6 Barrier Options

8.7 Lookbacks

8.8 Basket and Spread Options

8.9 Asian Options

8.10 Calculations in VBA

Problems

 9 More on Monte Carlo and Binomial Valuation

9.1 Monte Carlo Models for Path-Dependent Options

9.2 Binomial Valuation of Basket and Spread Options

9.3 Monte Carlo Valuation of Basket and Spread Options

9.4 Antithetic Variates in Monte Carlo

9.5 Control Variates in Monte Carlo

9.6 Accelerating Binomial Convergence

9.7 Calculations in VBA

Problems

 10 Finite Difference Methods

10.1 Fundamental PDE

10.2 Discretizing the PDE

10.3 Explicit and Implicit Methods

10.4 Crank-Nicolson

10.5 European Options

10.6 American Options

10.7 Barrier Options

10.8 Calculations in VBA

Problems

Part Ⅲ Fixed Income

 11 Fixed Income Concepts

11.1 The Yield Curve

11.2 LIBOR

11.3 Swaps

11.4 Yield to Maturity, Duration, and Convexity

11.5 Principal Components

11.6 Hedging Principal Components

Problems

 12 Introduction to Fixed Income Derivatives

12.1 Caps and Floors

12.2 Forward Rates

12.3 Portfolios that Pay Spot Rates

12.4 The Market Model for Caps and Floors

12.5 The Market Model for European Swaptions

12.6 A Comment on Consistency

12.7 Caplets as Puts on Discount Bonds

12.8 Swaptions as Options on Coupon Bonds

12.9 Calculations in VBA

Problems

 13 Valuing Derivatives in the Extended Vasicek Model

13.1 The Short Rate and Discount Bond Prices

13.2 The Vasicek Model

13.3 Estimating the Vasicek Model

13.4 Hedging in the Vasicek Model

13.5 Extensions of the Vasicek Model

13.6 Fitting Discount Bond Prices and Forward Rates

13.7 Discount Bond Options, Caps and Floors

13.8 Coupon Bond Options and Swaptions

13.9 Captions and Floortions

13.10 Yields and Yield Volatilities

13.11 The General Hull-White Model

13.12 Calculations in VBA

Problems

 14 A Brief Survey of Term Structure Models

14.1 Ho-Lee

14.2 Black-Derman-Toy

14.3 Black-Karasinski

14.4 Cox-Ingersoll-Ross

14.5 Longstaff-Schwartz

14.6 Heath-Jarrow-Morton

14.7 Market Models Again

Problems

Appendices

 A Programming in VBA

A.1 VBA Editor and Modules

A.2 Subroutines and Functions

A.3 Message Box and Input Box

A.4 Writing to and Reading from Cells

A.5 Variables and Assignments

A.6 Mathematical Operations

A.7 Random Numbers

A.8 For Loops

A.9 While Loops and Logical Expressions

A.10 If, Else, and ElseIf Statements

A.11 Variable Declarations

A.12 Variable Passing

A.13 Arrays

A.14 Debugging

 B Miscellaneous Facts about Continuous-Time Models

B.1 Girsanov's Theorem

B.2 The Minimum of a Geometric Brownian Motion

B.3 Bessel Squared Processes and the CIR Model

List of Programs

List of Symbols

References

Index