Derivatives Valuation and Risk Management

by Dubofsky, David A.; Miller, Thomas W.

• ISBN13: 9780195114706
• ISBN10: 0195114701
• Format: Hardcover
• Copyright: 2002-09-05
• Publisher: Oxford University Press

Summary

Derivatives: Valuation and Risk Management, by David A. Dubofsky and Thomas W. Miller, Jr., enables students to acquire a strong working knowledge and thorough understanding of the rapidly growing field of financial derivatives. Students will learn essential risk management skills, such as howmarkets in these securities can be used to shift risk away from or toward the user. With the purchase of this book, students will also have the unique opportunity to utilize Fincad XL-Dubofsky/Miller Edition, a limited version of FinancialCAD's comprehensive derivatives valuation toolkit, Fincad XL. The book features many examples using FinancialCAD's industry-leading package,affording students the chance to develop "real life" skills and helping business school students gain a competitive edge in the job market. Derivatives: Valuation and Risk Management is ideal for both undergraduate and graduate classes on derivatives, financial risk management, futures, or options. Fincad XL is a software product currently used by thousands of financial practitioners and companies worldwide. Functions available in Fincad XL-Dubofsky/Miller Edition include: DT Swaps DT Forward Rates DT Vanilla Options DT Exotic Options DT Fixed Income DT Interest Rate Derivatives To download your copy of Fincad XL-Dubofsky/Miller Edition, go to www.fincad.com/oxford. For more information on the complete version of Fincad XL, visit www.fincad.com.

Table of Contents

Preface	xxi
About the Authors	xxv
PART 1 INTRODUCTION TO DERIVATIVES AND RISK MANAGEMENT	1	(48)
An Overview of Derivative Contracts	3	(19)
Forward Contracts and Futures Contracts	4	(4)
Swaps	8	(6)
Options	14	(3)
Why Is It Important to Learn About Derivatives?	17	(1)
Summary	18	(4)
References	19	(1)
Notes	19	(1)
Problems	20	(2)
Risk and Risk Management	22	(27)
What Is Risk?	23	(1)
How Is Risk Measured?	24	(9)
Random Variables, Probability Distributions, and Variance	24	(4)
Measuring Risk Using Past Data	28	(2)
Identifying Risk Exposure	30	(3)
Should Firms Manage Risk?	33	(6)
Hedging Reduces the Expected Costs of Financial Distress	33	(1)
Hedging Makes It More Likely that Future Attractive Investments Will Be Made by the Firm	34	(1)
It Is Less Costly for the Firm to Hedge Than for Individuals to Hedge	35	(1)
Firms May Have Better Information than Individuals	35	(1)
Nonsystematic Risks Should Be Hedged When Owners Are Not Well Diversified	36	(1)
Hedging Can Increase Debt Capacity	36	(1)
Risk Management Can Reduce Taxes	36	(2)
Risk-Averse Managers Will Prefer to Hedge	38	(1)
Other Reasons for Using Derivatives	39	(1)
What Should Be Done After Risk Exposures Have Been Identified?	39	(1)
Accounting for Derivatives: FAS 133	40	(2)
Summary	42	(7)
Further Reading	42	(1)
References	43	(1)
Notes	44	(1)
Problems	45	(4)
PART 2 FORWARD CONTRACTS AND FUTURES CONTRACTS	49	(254)
Introduction to Forward Contracts	51	(17)
General Concepts	51	(5)
Forward Rate Agreements	56	(3)
Forward Foreign Exchange Contracts	59	(5)
Summary	64	(4)
Notes	64	(1)
Problems	65	(3)
Using Forward Contracts to Manage Risk	68	(19)
Using Forwards to Manage Commodity Price Risk	68	(5)
Buying Forwards to Hedge Against Price Increases	68	(2)
Selling Forwards to Hedge Against Price Declines	70	(3)
Using Forwards to Manage Interest Rate Risk	73	(4)
Hedging Against an Increase in Interest Rates	73	(3)
Hedging Against a Decline in Interest Rates	76	(1)
Using Forward Foreign Exchange Contracts to Manage Risk	77	(4)
Managing the Risk That the Price of a Foreign Currency Will Rise	77	(2)
Managing the Risk That the Price of a Foreign Currency Will Decline	79	(2)
What Quantity Should Be Bought or Sold Forward?	81	(1)
Summary	82	(5)
References	83	(1)
Notes	83	(1)
Problems	83	(4)
Determining Forward Prices and Futures Prices	87	(39)
Forward Commodity Prices	87	(4)
The Cost-of-Carry Model	87	(1)
Proof of the Cost-of-Carry Model	88	(2)
Examples	90	(2)
Transactions Costs	92	(2)
Implied Repo Rates and Implied Reverse Repo Rates	94	(2)
Forward Prices of Commodities: The Convenience Yield	96	(2)
Do Forward Prices Equal Expected Future Spot Prices?	98	(3)
Valuing a Forward Contract After Origination	101
Forward Exchange Rates	91	(17)
The Standard Approach to Deriving the Forward Exchange Rate	102	(2)
An Alternative Derivation of the Theoretical Forward Price	104	(3)
The Implied Repo Rate	107	(1)
Forward Interest Rates	108	(6)
Spot Rates and Forward Rates	108	(4)
How to Lock in a Forward Rate	112	(2)
Summary	114	(12)
References	115	(1)
Notes	115	(1)
Problems	116	(5)
Appendix A Selling Short	121	(2)
Appendix B Day Count Methods	123	(1)
Appendix C Computing the Future Value of Carry Return Cash Flows	124	(2)
Introduction to Futures	126	(39)
Futures Contracts and Forward Contracts	126	(2)
Margin Requirements for Futures Contracts	128	(2)
Marking to Market	130	(4)
Basis and Convergence	134	(3)
Should Futures Prices Equal Forward Prices?	137	(5)
Futures Contracts, Exchanges, and Regulation	142	(2)
The Purposes of Futures Markets	144	(1)
Reading Futures Prices in the Wall Street Journal	145	(6)
Commodity Futures	145	(2)
Financial Futures	147	(4)
Limits on Price Fluctuations	151	(1)
Orders and Position Limits	151	(3)
Individuals in the Futures Industry	154	(2)
Speculators	154	(1)
Hedgers	154	(1)
Arbitrageurs	154	(1)
Individuals on the Floor of an Exchange	155	(1)
Other Market Participants	155	(1)
Taxes and Commissions	156	(1)
Taxes	156	(1)
Commissions	157	(1)
Summary	157	(8)
References	157	(2)
Notes	159	(2)
Problems	161	(4)
Risk Management with Futures Contracts	165	(25)
Introduction	165	(5)
Some Special Considerations in Hedging with Futures	170	(2)
The Hedge Ratio	172	(9)
The Portfolio Approach to a Risk-Minimizing Hedge	172	(8)
Dollar Equivalency	180	(1)
Tailing the Hedge	181	(3)
Managing the Futures Hedge	184	(1)
Summary	185	(5)
References	185	(1)
Notes	186	(1)
Problems	187	(3)
Stock Index Futures	190	(35)
What Is An Index?	190	(8)
Price-Weighted Indexes: The Dow Jones Average	191	(2)
Value-Weighted Averages: The S&P 500 Stock Index	193	(2)
The Value Line Index	195	(3)
Pricing Stock Index Futures	198	(11)
An Illustration of Stock Index Futures Pricing	199	(2)
Synthetic Stock and Synthetic Treasury Bills	201	(1)
Transactions Costs: Commissions and Bid-Ask Spreads	202	(2)
More on Dividends	204	(2)
Program Trading	206	(3)
Risk Management with Stock Index Futures	209	(10)
Equity Risk	209	(2)
Adjusting the Beta of a Portfolio with Stock Index Futures	211	(5)
Stock Picking	216	(1)
An Anticipatory Hedge	217	(1)
Caveats About Hedging with Stock Index Futures	217	(1)
Using Stock Index Futures to Gain International Equity Exposure	218	(1)
Summary	219	(6)
References	219	(1)
Notes	220	(1)
Problems	221	(4)
Treasury Bond and Treasury Note Futures	225	(44)
Features of the T-Bond Futures Contracts	225	(9)
Reading Spot T-Bond Prices	227	(2)
Reading T-Bond and T-Note Futures Prices	229	(1)
The Delivery Process for T-Bond and T-Note Futures Contracts	229	(2)
Which T-Bonds Are Deliverable into the T-Bond Futures Contract?	231	(1)
Conversion Factors and Invoice Amounts	231	(2)
Computing the Conversion Factors	233	(1)
Determining T-Bond and T-Note Futures Prices	234	(10)
Determining the Cheapest-to-Deliver T-Bond or T-Note: Maximize the Raw Basis	235	(1)
Determining the Cheapest-to-Deliver T-Bond or T-Note: Maximize the Implied Repo Rate	236	(2)
Determining the Cheapest-to-Deliver T-Bond or T-Note by Using Duration	238	(1)
An Example of How to Determine the Cheapest-to-Deliver T-Bond	238	(2)
Determining the Theoretical T-Bond Futures Price	240	(2)
When Is Delivery Likely to Take Place?	242	(1)
The Short Timing and Quality Options	243	(1)
Using T-Bond Futures to Shift Interest Rate Risk	244	(8)
Hedging Fundamentals	244	(2)
Hedging Long Bond Position: A Short Hedge	246	(3)
Hedging Interest Rate Risk During a GIC Offering Period: A Long Hedge	249	(3)
Advanced Applications of T-Bond and T-Note Futures Contracts	252	(7)
Changing the Duration of a Portfolio	252	(2)
Synthetic Instruments	254	(1)
Asset Allocation	254	(4)
The NOB, FOB, FITE, and MOB Spreads	258	(1)
Summary	259	(10)
References	260	(1)
Notes	260	(2)
Problems	262	(3)
Appendix Duration and Convexity	265	(4)
Treasury Bill and Eurodollar Futures	269	(34)
The Spot Treasury Bill Market	269	(4)
T-Bill Futures Contracts	273	(1)
The Eurodollar Cash Market	274	(1)
Eurodollar Futures Contracts	275	(8)
Theoretical Pricing of Eurodollar Futures Contracts	276	(2)
Arbitrage Pricing of Eurodollar Futures Contracts	278	(5)
Two Useful Applications of Eurodollar Futures Contracts	283	(3)
Shortening the Maturity of a Eurodollar Time Deposit	284	(1)
Lengthening the Maturity of a Eurodollar Time Deposit	285	(1)
Hedging with Short-Term Interest Rate Futures	286	(10)
Short Hedge Situations	287	(1)
Long Hedge Situations	287	(1)
The Hedge Ratio	287	(1)
Using T-Bill Futures to Protect the Value of a Portfolio	288	(2)
Using Eurodollar Futures to Lock in a Single-Period Borrowing Rate	290	(2)
Using Eurodollar Futures to Lock in a Multiperiod Borrowing Rate	292	(3)
Choosing Between a Strip Hedge and a Stack Hedge	295	(1)
Eurodollar Bundles and Packs	296	(1)
Bundles	296	(1)
Packs	297	(1)
Summary	297	(6)
References	298	(1)
Notes	298	(1)
Problems	299	(4)
PART 3 SWAPS	303	(68)
An Introduction to Swaps	305	(20)
Interest Rate Swaps	305	(8)
An Example of a Plain Vanilla Fixed-for-Floating Interest Rate Swap	306	(1)
Generalizing the Plain Vanilla Fixed-Floating Interest Rate Swap	307	(2)
Characterizing a Fixed-Floating Interest Rate Swap as a Portfolio of FRAs	309	(2)
Characterizing a Fixed-Floating Interest Rate Swap as a Coupon-Bearing Asset Plus a Coupon-Bearing Liability	311	(1)
Quoting Prices of Plain Vanilla, Fixed-Floating Interest Rate Swaps	311	(1)
Other Interest Rate Swap Structures	312	(1)
Currency Swaps	313	(4)
An Example of a Fixed-Fixed Currency Swap	314	(1)
An Example of a Fixed-Floating Currency Swap	314	(2)
Other Currency Swap Structures	316	(1)
Commodity Swaps	317	(1)
Equity Index Swaps	317	(1)
Credit Risk in Swaps and Credit Swaps	318	(2)
Summary	320	(5)
References	321	(1)
Notes	321	(1)
Problems	322	(3)
Using Swaps to Manage Risk	325	(18)
Using Interest Rate Swaps	325	(8)
Swapping to Lower Borrowing Costs	325	(3)
Swapping to Hedge Against the Risk of Rising Interest Rates	328	(2)
Swapping to Hedge Against the Risk of Falling Interest Rates	330	(1)
Swaps, Gap Analysis, and Duration	331	(2)
Using Currency Swaps	333	(3)
Swapping to Lower Borrowing Costs in a Foreign Country	333	(2)
Swapping to Hedge Against the Risk of a Decline in a Revenue Stream	335	(1)
Swapping to Hedge Against the Risk of an Increase in Cost	335	(1)
Swapping to Hedge Against the Risk of a Decline in the Value of an Asset	335	(1)
Swapping to Hedge Against the Risk of a Rise in the Value of Liability	336	(1)
Using Commodity Swaps	336	(1)
Using Equity Swaps	337	(1)
Using Index Swaps	338	(1)
Using Diff Swaps	339	(1)
Summary	340	(3)
References	340	(1)
Notes	340	(1)
Problems	341	(2)
Pricing and Valuing Swaps	343	(28)
Pricing and Valuing Plain Vanilla Fixed-Floating Interest Rate Swaps	343	(11)
An Example of Fixed-Floating Interest Rate Swap Pricing	344	(1)
A Shortcut to Pricing At-Market Fixed-Floating Interest Rate Swaps at Origination	345	(1)
Valuing an Interest Rate Swap After Origination	346	(3)
Using FRAs and Futures to Price Swaps	349	(5)
Pricing a Currency Swap	354	(10)
An Example of Pricing a Fixed-Fixed Currency Swap	354	(2)
Pricing a Fixed-Floating Currency Swap	356	(3)
Valuing a Fixed-Floating Currency Swap After Origination	359	(2)
Pricing a Diff Swap	361	(3)
Pricing a Commodity Swap	364	(2)
Summary	366	(5)
Notes	366	(1)
Problems	367	(4)
PART 4 OPTIONS	371	(232)
Introduction to Options	373	(38)
Call Options	373	(2)
Put Options	375	(1)
In The Money, At the Money, Out of the Money	376	(1)
Intrinsic Value and Time Value	376	(1)
Payout Protection	377	(1)
Pricing at Expiration	378	(3)
Call Values at Expiration	378	(2)
Put Values at Expiration	380	(1)
A Brief Look at Option Pricing Before Expiration	381	(4)
Calls	381	(3)
Puts	384	(1)
Stock Options Markets	385	(5)
Strike Prices for Listed Stock Options	386	(1)
Expiration Dates for Listed Stock Options	387	(1)
Market Makers	388	(1)
The Role of the Options Clearing Corporation	389	(1)
Reading Options Prices in the Financial Press	390	(1)
Transaction Costs	391	(2)
Margin	393	(2)
Taxes	395	(2)
Index Options	397	(3)
Index Options Are Cash Settled	397	(2)
Timing Risks	399	(1)
Foreign Exchange Options	400	(1)
Futures Options	401	(4)
Other Options	405	(1)
Summary	405	(6)
References	406	(1)
Notes	406	(2)
Problems	408	(3)
Options Strategies and Profit Diagrams	411	(32)
Profit Diagrams for Long Stock and Short Stock	411	(2)
Long Calls	413	(1)
Writing a Naked Call	414	(1)
Long Puts	415	(1)
Writing Naked Put	415	(2)
Covered Call Writing	417	(3)
Vertical Spreads	420	(5)
Bullish Vertical Spread with Calls	420	(1)
Bullish Vertical Spread with Puts	421	(1)
Bearish Vertical Spread with Calls	422	(1)
Bearish Vertical Spread with Puts	423	(1)
Other Thoughts on Vertical Spreads	423	(2)
Straddles and Strangles	425	(3)
Synthetic Forward	428	(2)
Other Strategies	430	(2)
Rate-of-Return Diagrams	432	(1)
Profit Diagrams for Different Holding Periods	433	(1)
Several Caveats	434	(2)
Research on Option Strategies	436	(1)
Summary	437	(6)
References	437	(1)
Notes	438	(1)
Problems	439	(4)
Arbitrage Restrictions on Option Prices	443	(32)
Notation	444	(2)
Time	444	(1)
Interest Rates	444	(1)
Dividends	444	(2)
Pricing Restrictions for Calls	446	(10)
Upper Bound	446	(1)
Lower Bounds	446	(7)
Early Exercise of American Calls	453	(3)
Puts	456	(6)
Upper Bounds	456	(1)
Lower Bound for Puts on a Non-Dividend-Paying Stock	457	(2)
Lower Price Boundaries for Puts on Dividend-Paying Stocks	459	(2)
Early Exercise of American Puts	461	(1)
Put-Call Parity	462	(7)
European Options; No Dividends	462	(2)
European Options on Stocks That Pay Unknown Dividends	464	(1)
American Options on Non-Dividend-Paying Stocks	465	(2)
American Options on Stocks That Pay Unknown Dividends	467	(2)
Box Spreads Using European Options	469	(1)
Summary	470	(5)
References	470	(1)
Notes	471	(1)
Problems	472	(3)
The Binomial Option Pricing Model	475	(46)
A Quiz	475	(2)
Deriving the Binomial Option Pricing Model for Calls on Non-Dividend-Paying Stocks	477	(16)
Assumptions	477	(1)
The Derivation: One-Period Binomial Option Pricing Model	478	(3)
Risk Neutrality	481	(1)
The Two-Period Binomial Option Pricing Model	482	(4)
A Numerical Example of the Two-Period Binomial Option Pricing Model	486	(3)
The Multiperiod Binomial Option Pricing Model	489	(2)
A Numerical Example of the Multiperiod Binomial Option Pricing Model	491	(2)
Using the Binomial Option Pricing Model to Value Calls on Dividend-Paying Stocks	493	(10)
European Calls on Stocks That Pay a Discrete Percentage Dividend	493	(4)
European Calls on Stocks Paying a Discrete, Known Dividend Amount	497	(2)
American Calls on Stocks Paying a Given Dollar Dividend Amount	499	(4)
Puts	503	(6)
Simple Binomial Put Pricing	503	(2)
A Numerical Example of Binomial Put Pricing	505	(4)
Portfolio Insurance and Dynamic Trading	509	(4)
Other References on the Binomial Option Pricing Model and Dynamic Trading	513	(1)
Summary	514	(7)
References	514	(1)
Notes	514	(1)
Problems	515	(6)
Continuous Time Option Pricing Models	521	(42)
The Black--Scholes Option Pricing Model	521	(2)
Assumptions Behind the Black-Scholes Option Pricing Model	521	(1)
A Quick Discussion of the Importance of Lognormal Returns	522	(1)
The Variance of the Stock's Return Is Proportional to Time	522	(1)
The Black--Scholes Option Pricing Model and a Detailed Numerical Example	523	(3)
An Intuitive Look at the Black-Scholes Option Pricing Model	526	(1)
The Black--Scholes Option Pricing Model and European Put Prices	527	(1)
Two Handy Extensions of the Black-Scholes Option Pricing Model	528	(3)
Variant One: The Black-Scholes Option Pricing Model on Securities Paying Known, Discrete Dividends	528	(2)
Variant Two: The Black-Scholes Option Pricing Model on Securities Paying a Continuous Dividend Stream	530	(1)
European Puts with Known Dividends	531	(1)
The Relationship Between the Binomial Option Pricing Model and the Black--Scholes Option Pricing Model	531	(1)
The Nettlesome Task of Estimating a Security's Volatility, σ	532	(7)
Historical Volatility	532	(2)
Improving on the Estimate from Historical Data	534	(1)
Implied Volatility (IV)	534	(1)
Using Implied Volatility Estimates	535	(1)
Market Volatility Index (VIX)	536	(1)
The Volatility Smile and the Term Structure of Volatility	536	(3)
Generalizing the Black-Scholes Option Pricing Model	539	(1)
Options on Futures Contracts	539	(3)
Valuing European Futures Options	540	(1)
Valuing American Futures Options	541	(1)
Put--Call Parity for Options on Futures Contracts	542	(1)
Strategies That Use Options on Futures Contracts	542	(1)
American Call Options	542	(5)
Pseudo-American Call Model	543	(2)
American Puts	545	(2)
Summary	547	(16)
References	547	(1)
Notes	548	(2)
Problems	550	(3)
Appendix Notes on Continuous Compounding and Stock Return Distributions	553	(10)
Using Options for Risk Management	563	(40)
The Greeks	565	(5)
The Greeks for Black-Scholes Calls (a.k.a. ``No-Name,'' Theta, Rho, Vega, Delta, and Gamma)	565	(4)
The Greeks for Black-Scholes Option Pricing Model: Puts	569	(1)
The Importance of Delta	570	(3)
What Is Delta?	570	(2)
What Is Gamma?	572	(1)
Riskless Hedging	573	(6)
Position Deltas and Gammas	579	(9)
Position Deltas	579	(1)
Position Gammas	580	(2)
Generalized Portfolio Sensitivities	582	(3)
Time Spreads	585	(3)
Caps, Floors, and Collars: Using Options to Manage Interest Rate Risk	588	(5)
Caps	588	(2)
Floors	590	(1)
Collars	590	(1)
Valuing Caps, Floors, and Collars	591	(2)
Summary	593	(10)
References	597	(1)
Notes	597	(1)
Problems	598	(5)
PART 5 DERIVATIVE FRONTIERS	603	(34)
Current Topics in Risk Management	605	(32)
Value at Risk (VaR)	605	(8)
Background	605	(1)
The VaR Concept	606	(1)
Computing VaR	606	(4)
Stress Testing	610	(3)
Back Testing	613	(1)
Which VaR Calculation Is Best?	613	(1)
Credit Derivatives and Options on Debt Instruments	613	(9)
Credit Derivatives Background	613	(1)
Two Major Types of Credit Derivative	614	(1)
Other ``Event'' Derivatives	615	(1)
Options on Debt Instruments and Interest Rate Options	616	(3)
Options on Swaps	619	(3)
Exotic Options	622	(8)
Free-Range Exotic Options	622	(4)
Path-Dependent Options	626	(3)
Shouts and Ladders	629	(1)
Summary	630	(7)
References	631	(1)
Notes	632	(2)
Problems	634	(3)
Index	637