Derivatives Markets and Analysis E-Book

R. Stafford Johnson

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Serie: Bloomberg Professional
• Sprache: Englisch

Seitenzahl: 1273

Veröffentlichungsjahr: 2017

Beschreibung

A practical, informative guide to derivatives in the real world Derivatives is an exposition on investments, guiding you from the basic concepts, strategies, and fundamentals to a more detailed understanding of the advanced strategies and models. As part of Bloomberg Financial's three part series on securities, Derivatives focuses on derivative securities and the functionality of the Bloomberg system with regards to derivatives. You'll develop a tighter grasp of the more subtle complexities involved in the evaluation, selection, and management of derivatives, and gain the practical skillset necessary to apply your knowledge to real-world investment situations using the tools and techniques that dominate the industry. Instructions for using the widespread Bloomberg system are interwoven throughout, allowing you to directly apply the techniques and processes discussed using your own data. You'll learn the many analytical functions used to evaluate derivatives, and how these functions are applied within the context of each investment topic covered. All Bloomberg information appears in specified boxes embedded throughout the text, making it easy for you to find it quickly when you need or, or easily skip it in favor of the theory-based text. Managing securities in today's dynamic and innovative investment environment requires a strong understanding of how the increasing variety of securities, markets, strategies, and methodologies are used. This book gives you a more thorough understanding, and a practical skillset that investment managers need. * Understand derivatives strategies and models from basic to advanced * Apply Bloomberg information and analytical functions * Learn how investment decisions are made in the real world * Grasp the complexities of securities evaluation, selection, and management The financial and academic developments of the past twenty years have highlighted the challenge in acquiring a comprehensive understanding of investments and financial markets. Derivatives provides the detailed explanations you've been seeking, and the hands-on training the real world demands.

Leseprobe

Table of Contents

Cover

Title Page

Preface

Content

Acknowledgments

About the Author

PART 1: Futures and Forward Contracts

CHAPTER 1: Futures Markets

Introduction to Futures and Options Markets

The Nature of Futures Trading and the Role of the Clearinghouse

Types of Futures Contracts

The Organized Markets and Characteristics of Futures Trading

Commodity Futures Hedging

Commodity Speculating with Futures

Pricing Futures and Forward Contracts: Carrying‐Cost Model

Conclusion

Selected References

Problems and Questions

Bloomberg Exercises

CHAPTER 2: Currency Futures and Forward Contracts

Hedging with Foreign Currency Futures and Forward Contracts

Speculating with Foreign Currency Futures and Forward Contracts

Hedging and Speculating with Equivalent Money Market Positions

Carrying‐Cost Model for a Currency

Conclusion

Selected References

Problems and Questions

Bloomberg Exercises

CHAPTER 3: Equity Index Futures

Speculative Strategies

Hedging Equity Positions

Carrying‐Cost Model for an Equity Index

Non‐Equity Indexes

Conclusion

Selected References

Problems and Questions

Bloomberg Exercises

CHAPTER 4: Interest Rate and Bond Futures and Forward Contracts

Types of Interest Rate Futures and Forward Contracts

Speculating with Interest Rate and Bond Futures Contracts

Hedging with Interest Rate and Bond Futures Contracts

Pricing Interest Rate and Bond Futures

Conclusion

Selected References

Problems and Questions

Bloomberg Exercises

PART 2: Options Markets and Strategies

CHAPTER 5: Fundamentals of Options Trading

Option Terminology

Fundamental Option Strategies

Other Option Strategies

Option Price Relations

Put‐Call Parity

Option Exchanges

Conclusion

Selected References

Problems and Questions

Bloomberg Exercises

CHAPTER 6: Non‐Stock Options: Equity Index, Futures, OTC, and Embedded Options

Equity‐Index Options

Futures Options

Over‐the‐Counter Options

Convertible Securities

Embedded Options

Equity and Debt as Call Option Positions

Conclusion

Selected References

Problems and Questions

Bloomberg Exercises

CHAPTER 7: Option Strategies

Call Purchases

Call Purchases in Conjunction with Other Positions

Naked Call Writes

Covered Call Writes

Ratio Call Writes

Put Purchases

Naked Put Writes

Covered Put Writes

Ratio Put Writes

Call Spreads

Put Spreads

Straddle, Strip, and Strap Positions

Combinations

Condors

Simulated Stock Positions

Conclusion

Selected References

Problems and Questions

Bloomberg Exercises

CHAPTER 8: Option Hedging

Hedging Stock Portfolio Positions

Hedging Currency and Commodity Positions

Hedging Fixed‐Income Positions with Options

Conclusion

Selected References

Problems and Questions

Bloomberg Exercises

PART 3: Option Pricing

CHAPTER 9: Option Boundary Conditions and Fundamental Price Relations

Call Boundary Conditions

Put Boundary Conditions

Put and Call Boundary Conditions

Boundary Conditions Governing Non‐Stock Options

Conclusion

Selected References

Problems and Questions

Bloomberg Exercises

CHAPTER 10: The Binomial Option Pricing Model

Single‐Period BOPM

Multiple‐Period BOPM

Estimating the BOPM

Features of the BOPM

Conclusion

Selected References

Problems and Questions

Bloomberg Exercises

Appendix 10A: Risk‐Neutral Pricing

Risk‐Neutral Probability Pricing—Single‐Period Case

Risk‐Neutral Probability Pricing—Multiple‐Period Case

Appendix 10B: Discrete Dividend‐Payment Approach

Example

CHAPTER 11: The Black‐Scholes Option Pricing Model

The Black‐Scholes Call Model

The Black‐Scholes Put Model

Estimating the B‐S OPM

Applications of the OPM

Empirical Studies

Conclusion

Selected References

Problems and Questions

Bloomberg Exercises

CHAPTER 12: Pricing Non‐Stock Options and Futures Options

Pricing of Spot Index and Currency Options

Binomial Pricing of Futures Options

Pricing Equity Convertibles with the B‐S OPM

Greeks

Conclusion

Selected References

Problems and Questions

Bloomberg Exercises

CHAPTER 13: Pricing Bond and Interest Rate Options

The Binomial Interest Rate Model

Estimating the Binomial Interest Rate Tree

Pricing Bond and Interest Rate Options with the B‐S and Black OPMs

Conclusion

Selected References

Problems and Questions

Bloomberg Exercises

PART 4: Financial Swaps

CHAPTER 14: Interest Rate Swaps

Generic Interest Rate Swaps

Swap Markets

Swap Valuation

Comparative Advantage

Swap Applications

Forward Swaps

Swaptions

Non‐Generic Swaps

Conclusion

Selected References

Problems and Questions

Bloomberg Exercises

Appendix 14A: Valuation of Forward Swaps and Swaptions

CHAPTER 15: Credit Default and Currency Swaps

Generic Credit Default Swap

Currency Swaps

Conclusion

Selected References

Problems and Questions

Bloomberg Exercises

PART 5: Supplemental Appendixes

Appendix A: Overview and Guide to the Bloomberg System

Bloomberg System—Bloomberg Keyboard

Accessing Security Information

Indexes

Functionality

Economic, Industry, Law, and Municipal Information Screens

Monitor and Portal Screens

Portfolios and Baskets

Screening and Search Functions

The Bloomberg Excel Add‐In: Importing Bloomberg into Excel

Launchpad

Conclusion

Bloomberg Exercises

Appendix B: Directory Listing of Bloomberg Screens by Menu and Function

Appendix C: Uses of Exponents and Logarithms

Exponential Functions

Logarithms

Selected Reference

Index

End User License Agreement

List of Tables

Chapter 08

TABLE 8.1

TABLE 8.2

TABLE 8.3

TABLE 8.4

List of Illustrations

Chapter 01

EXHIBIT 1.1 Major Futures and Derivative Exchanges

EXHIBIT 1.2 Bloomberg Spot and Futures Corn Prices

EXHIBIT 1.3 Prices on July 2016 CBT Corn Futures Contracts and Yellow Corn Spot Prices, 7/1/15 to 7/15/16

EXHIBIT 1.4 NYMEX August 2016 Crude Oil Futures Contract and Spot Index, 7/15/16 Bloomberg Description Screen (CLQ6 <Comdty>, USCRWTIC <Index>)

EXHIBIT 1.5 CME October 2016 Cincinnati HDD Oil Futures Contract, 7/15/16 Bloomberg Description Screen (CJV6 <Index>)

EXHIBIT 1.6 Prices on NYMEX July 2016 Crude Oil Futures Contract and West Texas Spot Index, 7/17/15 to 7/1/16 Bloomberg GP Screens (CLQ6 <Comdty>, USCRWTIC <Index>)

EXHIBIT 1.11 2016 July Coffee Futures Contract Bloomberg Description Screen

EXHIBIT 1.13 Bloomberg Description Screen for December 2017 Gold Futures Contract and Prices on October 2015 Gold Futures, December 2017 Gold Futures, and Gold Spot 1/10/2014 to 2/16/2105

EXHIBIT 1.15 Regression Relation between Percentage Change in Gold Prices (XAU) and Silver Prices (XAG), 7/19/2014 to 7/18/16

EXHIBIT 1.16 Bloomberg Description Screen for Prices on July 2016 Silver Futures and July 2016 Gold Futures, 5/2/16 to 7/18/16

EXHIBIT 1.18 Bloomberg Grain and Cash and Carry Analysis Screen (GRCC) for Yellow Corn on 7/15/16 and Prices on September 2016 CBT Corn Futures Contracts and Yellow Corn Spot Prices, 7/20/15 to 7/14/16

EXHIBIT 1.19 Bloomberg Custom Chart Screen

Chapter 02

EXHIBIT 2.2 CME December British Pound Futures Contract Bloomberg Description and Price Screens, BPZ6 <Curncy>

EXHIBIT 2.3 Three‐Month British Pound Forward Rates Bloomberg Description and Price Screens, GBP3M <Curncy>

EXHIBIT 2.10 Regression Relation between British Pound (BP) and Australian Dollar (AUD)

EXHIBIT 2.11 Prices on June 2016 BP Futures Contracts and June 2016 AUD Futures Contracts, 1/4/16 to 6/13/16

Chapter 03

EXHIBIT 3.1 S&P 500 Futures Contract Bloomberg Description and Price Screens, SPA <Comdty>

EXHIBIT 3.4 Health Care Index and June Health Care Futures Contract Bloomberg Description and Price Screens

EXHIBIT 3.6 Regression Relation Between Health Care Index and Technology Index

EXHIBIT 3.7 Prices on June Technology Index Futures and Short in June Health‐Care Index Futures: 1/1/ 2016 to 6/6/16

EXHIBIT 3.12 Values of Xavier Growth Fund, Russell 1,000, and June Mini‐Russell 1,000 Futures Contract from 9/17/15 to 6/16/16

EXHIBIT 3.17 Index Arbitrage Using Proxy Portfolio When the S&P 500 Index Futures Are Overpriced

EXHIBIT 3.18 Index Arbitrage Using Proxy Portfolio When the S&P 500 Index Futures Are Underpriced

EXHIBIT 3.20 Values of Xavier Equity Index Fund, Russell 1,000 Growth Index (RLG), and June Mini‐Russell 1,000 Growth Index Futures Contract (RGYM6) from 12/1/15 to 6/16/16

EXHIBIT 3.22 CBOE’s Volatility Index and Futures Contracts

EXHIBIT 3.23 Example of PORT Slides—Xavier Growth Fund

EXHIBIT 3.24 Example of Bloomberg CIXB Screen

EXHIBIT 3.25 Example of Bloomberg OSA Screen

Chapter 04

EXHIBIT 4.2 CME’s December Eurodollar Futures Bloomberg Description Screens, Price and Yield Graphs

EXHIBIT 4.3 CME’s Five‐Year Eurodollar Bundle Contract Bloomberg Description Screens

EXHIBIT 4.4 CBT’s September US Ultra‐Treasury Bond Contract: Price and Yield Graphs

EXHIBIT 4.6 CBT’s September Five‐Year T‐Note Contract Bloomberg Description Screens, Price and Yield Graphs

EXHIBIT 4.8 Prices Graph on CBT September Five‐Year T‐Note Futures Contract (FVU6) and Yields on Five‐Year T‐Note (USGG5YR) Contracts 12/29/15 to 6/30/16

EXHIBIT 4.11 Yield Curves: On‐the‐Run and Off‐the‐Run US Treasury Yield Curve (I111)

EXHIBIT 4.12 Prices on June 2016 and September 2016 Ultra T‐Bond Futures Contract and Deliverable Bond, Treasury, 3

4/15/41

EXHIBIT 4.14 Yield Curves on 5/29/15 and 4/7/16 for the On‐the‐Run and Off‐the‐Run US Treasury Yield Curve (I111), Prices on September 2016 5‐Year T‐Note and 30‐Year T‐Bond Futures Contracts

EXHIBIT 4.16 Yield on the Constant Maturity Five‐Year Treasury Index, Prices on CBT June 2016 Five‐Year T‐Note Contract, and Prices on 1 3/8% Treasury with Maturity of 8/31/2020

EXHIBIT 4.17 Prices and Yields on CME’s June Eurodollar Futures

EXHIBIT 4.19 Six‐Month LIBOR (US0006M), Three‐Month LIBOR (US0006M), and Prices on CME’s December 2015 Eurodollar Futures (EDZ15) 9/15/2015 to 3/15/2016

EXHIBIT 4.22 Value of Xavier Bond Fund, Price of CBT June 2016 Five‐Year T‐Note Contract, and Yield on the Constant Maturity Five‐Year Treasury Index

EXHIBIT 4.24 Xavier Bond Fund and BOA/ML Aggregate Performance

EXHIBIT 4.27 Bloomberg Description and YAS Screens on 7/8/16 for US Treasury with 2.5% Coupon and Maturity 8/15/23

EXHIBIT 4.28 Example of DLV Screen

EXHIBIT 4.29 Example of PORT Screen: Xavier Bond Fund

EXHIBIT 4.30 Example of MARS Screens

Chapter 05

EXHIBIT 5.12 Price and Variability Relation for Stock A, Volatility: σ(Return) = 0.11

EXHIBIT 5.13 Price and Variability Relation for Stock B, Volatility: σ(Return) = 0.22

EXHIBIT 5.16 Bloomberg Description Screen for September 2016 85 P&G Call

EXHIBIT 5.17 Prices on September P&G 85 Call, September P&G 85 Put, and P&G Stock, 6/20/16 to 7/29/16

EXHIBIT 5.18 Example of Bloomberg Option Scenario Screen, OSA

Chapter 06

EXHIBIT 6.2 S&P 500 and NASDAQ 100 Options, 8/23/16

EXHIBIT 6.3 Option Price Curves: December 2,220 S&P 500 Call and December 4,100 NASDAQ 100 Put

EXHIBIT 6.5 Description Screen for December S&P 500 Futures Call:

X

= 2,155,

C

= 70.20; 8/4/16

EXHIBIT 6.6 Fundamental Futures Options Profit Graphs for December S&P 500 Futures

EXHIBIT 6.7 Description Screen and Profit Graph for December British Pound Futures Put:

X

= $1.30,

P

= $0.0252, Size = 62,500 BP, 8/6/16

EXHIBIT 6.8 Description Screen and Profit Graph for December Corn Futures Call:

X

= $3.30/bu.,

C

= $0.20/bu., Size = 5,000 bushels, 8/8/16

EXHIBIT 6.9 Description Screen and Profit Graph for December Crude Oil Futures Put:

X

= $45.00/brl.,

P

= $3.72 brl., Size = 1,000 brl., 8/8/16

EXHIBIT 6.10 Description Screen and Profit Graphs for December Five‐Year T‐Note Futures:

X

= $122,000, and Profit Graphs for Call Purchase, Naked Call Write, and Put Purchase with

C

= $2,130,

P

= $2,130

EXHIBIT 6.11 Description Screen and Profit Graph for December Eurodollar Futures Call:

X

= $998,125,

C

= 56.25, 8/6/16

EXHIBIT 6.12 Futures Call Price Curve

EXHIBIT 6.13 Futures Put Price Curve

EXHIBIT 6.14 Price Graphs: Five‐Year Constant Maturity US Treasury Yields (H15T5y), December 2016 Five‐Year T‐Note Futures (FVZ6), 122 December Five‐Year T‐Note Futures Call (FVZ6C122), and 122 December Five‐Year T‐Note Futures Put (FVZ6P122)

EXHIBIT 6.15 Interest Rate Call Option Purchase

EXHIBIT 6.16 Interest Rate Put Option Purchase

EXHIBIT 6.17 Select Warrants

EXHIBIT 6.18 GM Warrant (Gm/WS/B0:

X

= $18.33, Expiration = 7/10/19), Bloomberg Description Page, 8/12/16, Price Graph of GM Warrant and GM Stock, 8/12/11 to 8/12/16

EXHIBIT 6.19 Warrant Profit Graph and Price Graph

EXHIBIT 6.20 Rights of Empire Resort Inc.: Empire Right: Subscription Price = $14.40, One right for 0.4748644 Shares

EXHIBIT 6.21 Select Convertible Bonds

EXHIBIT 6.22 Centerpoint Energy Convertible Bond (CNP CUSIP: US15189T20690): Coupon = 4.1837%, Maturity = 09/15/16, CR = 1.00), Bloomberg Description and YAS Screens, 8/12/16

EXHIBIT 6.23 Equity and Debt Values at Maturity

EXHIBIT 6.24 Equity and Debt Values Prior to Maturity

Chapter 07

EXHIBIT 7.11 Price Graphs: Devon Energy, Devon April 24 Put, Devon April 20 Put, and Devon April 26 Put, 1/15/16 to 3/28/16

EXHIBIT 7.23 Straps with Different Ratios

Chapter 08

EXHIBIT 8.20 Evaluating a Commodity Purchase Position Hedged with Futures Options

EXHIBIT 8.21 Importing Equity Portfolios into Bloomberg’s Option Scenario Screen and Adding Options

EXHIBIT 8.22 Importing Cheapest‐to‐Deliver‐Note into Bloomberg’s MARS Screen and Adding T‐Note Futures and Futures Options

EXHIBIT 8.23 Importing Bond Portfolios into Bloomberg’s MARS Screen and Adding Options

Chapter 09

EXHIBIT 9.19 Arbitrage Using Proxy Portfolio when the Put‐Call‐Parity Condition for Index Options Is Violated

EXHIBIT 9.23 Chart Screen

EXHIBIT 9.24 OMON

Chapter 10

EXHIBIT 10.1 Single‐Period Binomial Values of Stock, Call, and Replicating Portfolio:

S

0

= $50,

u

= 1.1,

d

= 0.95,

R

f

= 0.025

EXHIBIT 10.4 Single‐Period Binomial Values of Stock, Put, and Replicating Portfolio:

S

0

= $50,

u

= 1.1,

d

= 0.95,

R

f

= 0.025

EXHIBIT 10.7 Single‐Period Binomial Values of Stock, Call, and Replicating Portfolio When Stock Pays Dividend:

S

0

= $50,

u

= 1.1,

d

= 0.95,

D

1

= $0.50,

R

f

  = 0.025

EXHIBIT 10.10 Two‐Period Binomial Values of Stock,

u

= 1.0488,

d

= 0.9747, and

n

= 2

EXHIBIT 10.11 Two‐Period Binomial Values of Stock, Call, and Replicating Portfolios:

S

0

= $50,

u

= 1.0488,

d

= 0.9747,

R

f

= 0.0125,

n

= 2

EXHIBIT 10.12 Two‐Period Binomial Values of Stock, Put, and Replicating Portfolios:

S

0

= $50,

u

= 1.0488,

d

= 0.9747,

R

f

= 0.0125,

n

= 2

EXHIBIT 10.13 Two‐Period Binomial Values of American Put:

S

0

= $50,

u

= 1.0488,

d

= 0.9747,

R

f

= 0.0125,

n

= 2

EXHIBIT 10.14 Two‐Period Binomial Values of Stock, when Stock Pays Dividend:

S

0

= $50,

u

= 1.0488,

d

= 0.9747,

D

1

= $0.50, and Ex‐Dividend in Period 1,

R

f

= 0.0125

EXHIBIT 10.15 Merton's Dividend‐Adjusted Binomial Model

S

0

= $20,

u

= 1.09356,

d

= 0.9144,

ψ

= 3%,

R

A

= 2.5%,

n

= 5, Δ

t

= 0.20

EXHIBIT 10.16 Binomial Process of Stock Prices and Logarithmic Returns

EXHIBIT 10.18 Binomial Prices of American and European Calls and Puts for

n

= 6

EXHIBIT 10.19 BOPM Call Price, Put Price, and Stock Price Relations for Different Parameter Values

EXHIBIT 10.20 HVG Screens

EXHIBIT 10.21 BDVD Screen

EXHIBIT 10.22 FIT Screen

EXHIBIT 10.23 DES, CALL, and OVDV Screens

EXHIBIT 10.24 BOPM Excel Program

Chapter 11

EXHIBIT 11.2 B‐S OPM Option Price and Stock Price Relation Given Different Parameter Values

EXHIBIT 11.3 Volatility Smile

EXHIBIT 11.4 Volatility Term Structures

EXHIBIT 11.5 Volatility Surface, P&G, 11/11/16

EXHIBIT 11.6 Option Profit Graphs at Expiration and Prior to Expiration: Stock Price = $50,

X

= $50,

σ

= 0.30,

R

f

= 0.025,

t

= 0.5,

t

1

= 0.25

EXHIBIT 11.8 Neutral Delta Position with Positive Gamma

EXHIBIT 11.9 OVME for P&G Call: 11/29/2016:

X

= 82.50, Expiration = 2/17/17

EXHIBIT 11.10 Volatility Tab

EXHIBIT 11.11 Scenario Tab

EXHIBIT 11.12 Backtest Tab

EXHIBIT 11.13 Exhibit OVME Setting Tab

Chapter 12

EXHIBIT 12.1 Merton's Dividend‐Adjusted Binomial Model

S

0

= $2,500,

σ

= 0.30,

μ

= 0.00,

ψ

= 4%,

R

A

= 6%,

n

= 5,

t

= 180/365, Δ

t

=

t/n

= 0.09863,

X

= 2,500,

u

= 1.09880,

d

= 0.9101,

p

= 0.48693

EXHIBIT 12.6 OVME for S&P 500 Spot Index: 12/14/16,

S

0

= 2,269.27,

X

= 2,270, Expiration = 3/17/17 (SPX C2270 3/17/17 <Index>, OVME)

EXHIBIT 12.7 OVME for March S&P 500 Futures Contract: 12/14/16,

f

0

= 2,265,

X

= 2,265, Expiration = 3/17/17, European (SPH7 <Comdty>, OVME).

EXHIBIT 12.8 OV for March 2017 British Pound Futures Contract: 12/14/16,

f

0

= $1.2698/BP,

X

= $1.27, Expiration = 3/17/17, American (BPH7 <Curncy>, OV)

EXHIBIT 12.9 OV for March 2017 Crude Oil Futures Contract: 12/14/16,

f

0

= $53.75,

X

= $53, Expiration = 3/17/17, American (CLH7C 53 <Comdty>, OV)

EXHIBIT 12.10 OVME, Warrants

Chapter 13

EXHIBIT 13.1 Binomial Tree of Spot Rates:

u

= 1.1,

d

= 0.95,

S

0

= 5%

EXHIBIT 13.2 Binomial Value of Bond Maturing in Three Periods: Coupon = 5%, Face Value = 100, Maturity = Three Periods,

u

= 1.1,

d

= 0.95,

S

0

= 5%

EXHIBIT 13.3 Binomial Value of Call Option on a Bond: Coupon = 5%, Face Value = 100, Maturity = 3 Periods, Call Option:

X

= 100, Expiration = 2 Periods,

u

= 1.1,

d

= 0.95,

S

0

= 5%

EXHIBIT 13.4 Binomial Value of Put Option on a Bond: Coupon = 5%, Face Value = 100, Maturity = Three Periods, Put Option:

X

= 100, Expiration = 2 Periods,

u

= 1.1,

d

= 0.95,

S

0

= 5%

EXHIBIT 13.5 Binomial Tree Valuation of Bond, Spot Options, Futures, and Futures Options

EXHIBIT 13.6 Binomial Trees for Zero Coupon Bonds, Implied Spot Rates for the Case:

u

and

d

Inversely Proportional and

q

= 0.5,

u

= 1.10,

d

= 1/

u

= 0.9091,

q

= 0.5

EXHIBIT 13.7 Binomial Tree Valuation of T‐Bill Futures and Futures Options

EXHIBIT 13.8 Binomial Tree: Caplet and Floorlet

EXHIBIT 13.9 Binomial Value of Callable Bond: Coupon = 5%, Face Value = 100, Maturity = 3 Periods, Call Price =

CP

=100,

u

= 1.1,

d

= 0.95,

S

0

= 5%

EXHIBIT 13.10 Binomial Value of Putable Bond: Coupon = 5%, Face Value = 100, Maturity = 3 Periods, Put Price =

PP

= 100,

u

= 1.1,

d

= 0.95,

S

0

= 5%

EXHIBIT 13.11 Binomial Value of a Convertible Bond

EXHIBIT 13.12 Binomial Value of Bond, Futures, and Futures Options for

n

= 30‐Period Case

EXHIBIT 13.13 Binomial Values of T‐Bill Futures and Futures Options:

n

= 8 Periods

EXHIBIT 13.14 Binomial Values of a Floorlet and Caplet:

n

= 8 Periods

EXHIBIT 13.15 Calibration Model

EXHIBIT 13.16 Calibration Model: 30‐Period Case

EXHIBIT 13.17 Pricing a Cap

EXHIBIT 13.18 OVME for Call Option on Five‐Year T‐Note Futures Contract: 1/23/17; Futures:

f

0

= 117 ‐24, Expiration = March; Call Option:

X

= 117 ‐ 24, Expiration = 3/31/17, Volatility = 3.694%, American, and Black OPM Value = 0.6183.

EXHIBIT 13.19 OVME for Call Option on Eurodollar Futures Contract: 1/23/17; Futures:

f

0

= 98.752, Expiration = 6/19/17; Call Option:

X

= 98.752, Expiration = 6/19/2017, Volatility = 0.309%, American, and Black OPM Value = 0.0784.

EXHIBIT 13.20 BVAL Screen: Intel Convertible Bond

EXHIBIT 13.21 SWPM: Cap Valuation

Chapter 14

EXHIBIT 14.5 Swap Market Structure

EXHIBIT 14.8 Fixed/Floating Swap

EXHIBIT 14.9 Payer Swaption

EXHIBIT 14.10 Fixed‐Rate Payer Swap

EXHIBIT 14.11 MARS Scenario Analysis without Swap

EXHIBIT 14.12 MARS Scenario Analysis with Fixed‐Payer Swap

EXHIBIT 14.13 Payer Swaption

EXHIBIT 14.14 MARS Scenario Analysis with Payer Swaption

Chapter 15

EXHIBIT 15.2 Currency Swap

EXHIBIT 15.5 Swap Bank Hedge: Swap Bank Issues Five‐Year, 4%, £100 Million Loan, Swaps It for Five‐Year, 6%, $150 Million Loan from US Company, and Purchases Five‐Year, 6%, $150 Million Bond

EXHIBIT 15.6 Swap Cash Flows and Swap Value

EXHIBIT 15.7 Swap Value: Four‐Year Swap with Rate on Dollars at 6.5%

EXHIBIT 15.8 CDSW: Macy's

EXHIBIT 15.9 SECF Screen

EXHIBIT 15.10 WCDS Screen

EXHIBIT 15.11 SWPM Screen

Appendix A

EXHIBIT A.1 Bloomberg Description (DES) and Price Graph (GP)

EXHIBIT A.2 Bloomberg Menu and Description (DES) for a Bond

EXHIBIT A.3 Bloomberg Government Bond Ticker Symbols: <GOVT> TK <Enter>

EXHIBIT A.4 Bloomberg Government Bond Description Slide

EXHIBIT A.5 Bloomberg Index Search (SECF)

EXHIBIT A.6 Bloomberg DES and MEMB Screens for Russell 3,000

EXHIBIT A.7 Bloomberg's Financial Analysis (FA) Screen, Macy's

EXHIBIT A.8 Bloomberg's Relative Valuation (RV) Screen, Macy's

EXHIBIT A.9 Bloomberg's Graphical Financial Analysis (GF) Screen, Macy's

EXHIBIT A.10 Bloomberg's ECST Screen

EXHIBIT A.11 Bloomberg's ECO Screen

EXHIBIT A.12 Bloomberg's ECOF

EXHIBIT A.13 Bloomberg's Sector and Industry Information (BI) and Economics (BIE) Screens

EXHIBIT A.14 Bloomberg IMAP Screen

EXHIBIT A.15 Bloomberg Country Information and Indicators, COUN

EXHIBIT A.16 Bloomberg's EVTS Screen

EXHIBIT A.17 Creating a Portfolio: PRTU Screen

EXHIBIT A.18 Portfolio Analysis Screen: PORT, Characteristics Tab

EXHIBIT A.19 GP and HRA Screen for CIXB‐Created Portfolio

Guide

Cover

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The Bloomberg Financial Series provides both core reference knowledge and actionable information for financial professionals. The books are written by experts familiar with the work flows, challenges, and demands of investment professionals who trade the markets, manage money, and analyze investments in their capacity of growing and protecting wealth, hedging risk, and generating revenue.

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DERIVATIVES MARKETS AND ANALYSIS

R. Stafford Johnson

Copyright © 2017 by R. Stafford Johnson. All rights reserved.

Published by John Wiley & Sons, Inc., Hoboken, New Jersey.

Published simultaneously in Canada.

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Library of Congress Cataloging‐in‐Publication Data is Available

ISBN 978‐1‐118‐20269‐2 (Hardcover)ISBN 978‐1‐118‐22828‐9 (ePDF)ISBN 978‐1‐118‐24072‐4 (ePub)

Cover Design: C. WallaceCover Images: Abstract Background© iStockphoto / jcarroll‐images;Chart Courtesy of R. Stafford Johnson

This book is dedicated to Nancy Shiels—My beacon

Preface

In 1973, the Chicago Board of Trade formed the Chicago Board Options Exchange (CBOE). The CBOE was the first organized option exchange for the trading of options. Just as the Chicago Board of Trade had served to increase the popularity of futures, the CBOE helped to increase the trading of options by making the contracts more marketable. Since the creation of the CBOE, organized stock exchanges in the United States, most of the organized futures exchanges, and many security exchanges outside the United States also began offering markets for the trading of options. As the number of exchanges offering options increased, so did the number of securities and instruments with options written on them. Today, option contracts exist not only on stocks but also on currencies, indexes, futures contracts, and debt and interest rate‐sensitive securities. There is also a large over‐the‐counter option market in currency, debt, and interest‐sensitive securities and products in the United States and a growing over‐the‐counter option market outside the United States. Just as impressive as the growth in options trading has been the growth in the futures market. Today, there are futures contracts on commodities, equity indexes, currencies, bonds, and interest rates, as well as such hybrid contracts as swaps. Options, futures, and swaps are derivatives—securities that derive their values from the underlying asset. Derivatives are used by institutional investors, portfolio managers, and corporations for speculation and hedging, as well as financial engineering in creating structured currency, equity, and debt positions.

Over the past 50 years, the investment industry has seen not only the proliferation of derivative securities and markets, but also academic contributions to the study of derivatives: The Black‐Scholes Option Pricing Model, index arbitrage, financial engineering, and dynamic portfolio insurance. The growth in the derivative markets and the academic contributions together point out the challenges in mastering an understanding and developing a knowledge of derivatives. The purpose of this text is to provide professionals and finance students with an exposition on derivatives that will take them from the basic concepts, strategies, and fundamentals to a more detailed understanding of the markets, advanced strategies, and models.

Derivative Markets and Analysis is the last in a three‐part series on securities from Bloomberg Press’s Financial Series. The first, Debt Markets and Analysis, covered fixed‐income securities, and the second, Equity Markets and Analysis, focused on stock and stock portfolios. This book covers subjects presented in many derivative texts: futures and forward markets, the carrying‐cost model for pricing futures, option strategies, the Black‐Scholes and Binomial Option Pricing models, futures options, and swaps.

Today, many practitioners manage their securities and portfolios using a Bloomberg terminal. Bloomberg is a computer information and retrieval system providing access to financial and economic data, news, and analytics. Bloomberg terminals are common on most trading floors and are becoming more common in universities where they are used for research, teaching, and managing student investment funds. Given this widespread use of the Bloomberg system, the text also provides guides for using Bloomberg data and analytical functions for the topics covered in each chapter. There are also supplemental appendices with detailed descriptions of the Bloomberg system and a listing of many of the analytical functions that can be applied to investment analysis.

It is my hope that the synthesis of fundamental and advanced topics with Bloomberg information and analytics will provide professionals and students of finance not only with a better foundation in understanding the complexities and subtleties of derivatives, but also with the ability to apply that understanding to real‐world investment decisions—to grasp how “it is done on the street.” It is also my hope that the integration of Bloomberg with derivative concepts and theories enhances the readers’ intellectual depth and understanding of finance. Finance and economics professors frequently require that students explain a theory, strategy, or idea mathematically, graphically, and intuitively. By so doing, students’ depth of understanding, as well as retention, of the theory and idea is often enhanced. It has been my experience in using Bloomberg in my derivatives classes that it too enhances a student’s depth and knowledge of derivatives.

The book is designed for professors offering a one‐semester derivatives course. The Bloomberg material is presented at the end of each chapter, allowing the material to be presented separately. The book is also written for professionals in the investment industry. For professionals, the text can be used as an instructional source and as a guide on how to apply Bloomberg to derivative markets and analysis, as well as a review of fundamental derivative concepts and theories.

Content

The book is comprehensive, covering derivative securities and markets, the major theories and models, and the practical applications of the models. The book is divided into five parts: Part 1 deals with the markets and strategies associated with futures and forward contracts; Part 2 examines options markets and strategies; Part 3 examines the pricing of options; Part 4 examines financial swaps; and Part 5 provides supplemental appendices.

Part 1 consists of four chapters. Chapter 1 examines the markets, uses, and pricing of commodity futures contracts. Chapter 2 covers futures and forward contracts on currency. Chapter 3 focuses on equity index contracts, and Chapter 4 covers interest rate and bond contracts.

Part 2 consists of four chapters. Stock options are examined in Chapter 5 in terms of fundamental option strategies and the functions and operations of the option exchange. The markets and uses of non‐stock options are explored in Chapter 6: equity‐index options, futures options, over‐the‐counter options, convertible securities, and embedded options. In Chapter 7, option analysis is expanded with a more detailed examination of the fundamental strategies and an analysis of other strategies. Finally, in Chapter 8, the hedging uses of options are explored.

Part 3 consists of five chapters. In Chapter 9, the fundamental option pricing relationships and option boundary conditions are presented. The Binomial Option Pricing model is derived in Chapter 10, and the seminal Black‐Scholes option pricing model is presented in Chapter 11. In Chapter 12, the pricing of non‐stock options is examined: spot indexes, currency options, futures options, and convertibles. The pricing of bond and interest rate options is examined using the binomial interest rate model in Chapter 13.

Part 4 consists of two chapters on financial swaps. The markets, uses, and pricing of generic interest rate swaps, forward swaps, and swaptions are presented in Chapter 14, and the markets, uses, and pricing of credit default swaps and currency swaps are the focus of Chapter 15.

The text stresses concepts, model construction, numerical examples, and Bloomberg applications and information sources. The text also includes end‐of‐the‐chapter problems and Bloomberg exercises. The Bloomberg exercises are designed for practitioners who have access to such terminals at their jobs, for professors and students who have access to Bloomberg terminals at their universities, and for students who have access to Bloomberg either at their university or possibly through internships they may have at financial companies. As I noted previously, it is my hope that the Bloomberg exercises will add depth to one’s understanding of derivatives, as well as an appreciation of the breadth of financial information and analytics provided by the Bloomberg system. Students are invited to visit www.wiley.com for additional materials, such as Excel spreadsheet programs that can be used to solve a number of the problems at the end of the chapters and videos that explain how to work some Bloomberg exercises. Also located at the Wiley website is an instructor site that includes chapter PowerPoint slides and an instructor’s manual with solutions to end‐of‐the‐chapter problems.

The book draws some material from some of my earlier texts: Debt Markets and Analysis, Equity Markets and Analysis, and Introduction to Derivatives. The Bloomberg material presented here comes from knowledge gained from using the terminal (or learned from my students who used Bloomberg) when I was the fund professor for the student equity investment fund and bond investment fund at Xavier University.

Acknowledgments

Many people have contributed to this text. First, I wish to personally thank Stephen Smith, Brandywine Global Investment Management, and the Smith Center for the Study of Capitalism and Society for their backing and support. I also thank my colleagues and students at Xavier University for their many years of support and encouragement. My appreciation is extended to the editors and staff at John Wiley & Sons, Inc., particularly Bill Falloon, executive editor; Jeremy Chia, project editor; Sharmila Srinivasan, production editor; and Cheryl Ferguson, copy editor. My appreciation is also extended to Stephen Isaacs, Bloomberg Press, for his support, help, and encouragement on this project.

I also wish to thank my children and their spouses, Wendi, Jamey, Matt, Shayna, and Scott, and my grandchildren, Bryce, Kendall, Malin, Kylee, and Ryan, and Mary Frances Johnson and Marlyn Erhart for their support, encouragement, and understanding. I also would like to recognize the pioneers in the academic study of derivatives: Fischer Black, Myron Scholes, Robert Merton, Stephen Ross, Mark Rubinstein, and others cited in the pages that follow. Without their contributions, this text could not have been written. Finally, I extend my gratitude to the many people who make up the soul of the Bloomberg system—analysts, programmers, systems experts, reps, and journalists. It is truly a remarkable system.

I encourage you to send your comments and suggestions to me: [email protected].

R. Stafford JohnsonXavier University

About the Author

R. Stafford Johnson is Professor of Finance and Director of the Smith Center for the Study of Capitalism and Society at the Williams College of Business, Xavier University. He is the author of six books: Options and Futures; Introduction to Derivatives; two editions of Bond Evaluation, Selection, and Management; Debt Markets and Analysis; and Equity Markets and Portfolio Analysis. He has also authored or co‐authored over 50 academic articles. His Equity Markets and Portfolio Analysis and Debt Markets and Analysis texts are core equity and fixed‐income investment books that cover extensively the functionality of Bloomberg terminals and its applicability to investments.

PART 1Futures and Forward Contracts

CHAPTER 1Futures Markets

In the mid‐1800s, Chicago was the transportation and distribution center for agriculture products. Farmers in the Midwest transported and sold their products to wholesalers and merchants in Chicago, who often would store and later transport the products by either rail or the Great Lakes to population centers in the East. Because of the seasonal nature of grains and other agriculture products and the lack of adequate storage facilities, farmers and merchants began to use forward contracts as a way of avoiding storage costs and pricing risk. These contracts were agreements in which two parties agreed to exchange commodities for cash at a future date, but with the terms and the price agreed upon in the present. An Ohio farmer in June might agree to sell his expected wheat harvest to a Chicago grain dealer in September at an agreed‐upon price. This forward contract enabled both the farmer and the dealer to lock in the September wheat price in June. In 1848, the Chicago Board of Trade (CBT) was formed by a group of Chicago merchants to facilitate the trading of grain. This organization subsequently introduced the first standardized forward contract, called a “to‐arrive” contract. Later, it established rules for trading the contracts and developed a system in which traders ensured their performance by depositing good‐faith money to a third party. These actions made it possible for speculators as well as farmers and dealers who were hedging their positions to trade their forward contracts. By definition, futures are marketable forward contracts. Thus, the CBT evolved from a board offering forward contracts to the United States’ first organized exchange listing futures contracts—a futures exchange.

Introduction to Futures and Options Markets

Futures and options contracts on stock, debt, and currency, as well as such hybrid derivatives as swaps, interest rate options, caps, and floors, are an important risk‐management tool. Farmers, portfolio managers, multinational businesses, and financial institutions often buy and sell derivatives to hedge positions they have in the derivative’s underlying asset against adverse price changes. Derivatives also are used for speculation. Many investors find buying or selling options or taking futures positions an attractive alternative to buying or selling the derivative’s underlying security. Finally, many institutional investors, portfolio managers, and corporations use derivatives for financial engineering, combining their debt, equity, or currency positions with different derivatives to create a structured investment or debt position with certain desired risk‐return features.

This book is an exposition on derivatives, describing the markets in which derivatives are traded, how they are used for speculating, hedging, and financial engineering, and how their prices are determined. Part 1 examines the markets, strategies, and pricing of futures and forward contracts, while Parts 2 and 3 focus on options contracts and pricing. Part 4, in turn, examines the swap market.

Overview of Futures Markets

As new exchanges were formed in New York, London, Singapore, and other large cities throughout the world, the types of futures contracts grew from grains and agricultural products to commodities and metals and finally to financial futures: futures on foreign currency, debt securities, and security indexes. Because of their use as a hedging tool by financial managers and investment bankers, the introduction of financial futures in the early 1970s led to a dramatic growth in futures trading. The financial futures market formally began in 1972 when the Chicago Mercantile Exchange (CME) created the International Monetary Market (IMM) division to trade futures contracts on foreign currency. In 1976, the CME extended its listings to include a futures contract on a Treasury bill. The CBT introduced its first futures contract in October 1975 with a contract on the Government National Mortgage Association (GNMA) pass‐through, and in 1977, it introduced the Treasury bond futures contract. The Kansas City Board of Trade was the first exchange to offer trading on a futures contract on an equity index, when it introduced the Value Line Composite Index (VLCI) contract in 1983. This was followed by the introduction of the Standard & Poor’s (S&P) 500 futures contract by the CME and the New York Stock Exchange (NYSE) index futures contract by the New York Futures Exchange (NYFE).

Whereas the 1970s marked the advent of financial futures, the 1980s saw the globalization of futures markets with the openings of the London International Financial Futures Exchange (LIFFE) in 1982, Singapore International Monetary Market in 1986, and the Toronto Futures Exchange in 1984. The increase in the number of futures exchanges internationally led to a number of trading innovations: electronic trading systems, 24‐hour worldwide trading, and alliances between exchanges. Concomitant with the growth in future trading on organized exchanges has been the growth in futures contracts offered and traded on the over‐the‐counter (OTC) market. In this market, dealers offer and make markets in more tailor‐made forward contracts in currencies, indexes, and various interest rate products. The combined growth in the futures and forward contracts has also created a need for more governmental oversight to ensure market efficiency and to guard against abuses. In 1974, Congress created the Commodity Futures Trading Commission (CFTC) to monitor and regulate futures trading. In that legislation, Congress also allowed the creation of self‐regulatory organizations, and in 1982, the National Futures Association (NFA), an organization of futures market participants, was established to oversee futures trading. Finally, the growth in futures markets led to the consolidation of exchanges. In 2006, the CME and the CBT approved a deal in which the CME acquired the CBT, forming the CME Group, Inc. With this and other consolidations, the major exchanges today offering derivatives include CBT/CME, Eurex, ICE, Hong Kong Futures Exchange, Singapore Exchange, Dubai Mercantile Exchange, Bolsa De Mercadorias & Futuros, and the Australian Stock Exchange. Exhibit 1.1 shows the Bloomberg CTM screen that lists the major exchanges trading futures and derivatives today.

EXHIBIT 1.1 Major Futures and Derivative Exchanges

Formally, a forward contract is an agreement between two parties to trade a specific asset at a future date with the terms and price agreed upon today. A futures contract, in turn, is a “marketable” forward contract, with marketability (the ease or speed in trading a security) provided through futures exchanges that not only list hundreds of contracts that can be traded but provide the mechanisms for facilitating the trades. Futures and forward contracts are known as derivative securities. A derivative security is one whose value depends on the values of another asset (e.g., the price of the underlying commodity or security). Another important derivative is an option. An option is a security that gives the holder the right, but not the obligation, to buy or sell a particular asset at a specified price on, or possibly before, a specific date.

Overview of Options Markets

Like the futures market, the US options market can be traced back to the 1840s when options on agriculture commodities were traded in New York. These option contracts gave the holders the right, but not the obligation, to purchase or to sell a commodity at a specific price on or possibly before a specified date. Like forward contracts, options made it possible for farmers or agriculture dealers to lock in future prices. In contrast to commodity futures trading, however, the early market for commodity options trading was relatively thin. The market did grow marginally when options on stocks began trading on the over‐the‐counter (OTC) market in the early 1900s. This market began when a group of investment firms formed the Put and Call Brokers and Dealers Association. Through this association, an investor who wanted to buy an option could do so through a member who either would find a seller through other members or would sell (write) the option himself.

The OTC option market was functional, but suffered because it failed to provide an adequate secondary market. In 1973, the CBT formed the Chicago Board Options Exchange (CBOE). The CBOE was the first organized option exchange for the trading of options. Just as the CBT had served to increase the popularity of futures, the CBOE helped to increase the trading of options by making the contracts more marketable. Since the creation of the CBOE, organized stock exchanges in the United States, most of the organized futures exchanges, and many security exchanges outside the United States also began offering markets for the trading of options. As the number of exchanges offering options increased, so did the number of securities and instruments with options written on them. Today, option contracts exist not only on stocks but also on foreign currencies, indexes, futures contracts, and debt and interest rate‐sensitive securities.

In addition to options listed on organized exchanges, there is also a large OTC market in currency, debt, and interest‐sensitive securities and products in the United States and a growing OTC market outside the United States. OTC debt derivatives are primarily used by financial institutions and nonfinancial corporations to manage their interest rate positions. The derivative contracts offered in the OTC market include spot options and forward contracts on Treasury securities, London Interbank Offered Rate–related (LIBOR‐related) securities, and special types of interest rate products, such as interest rate calls and puts, caps, floors, and collars. OTC interest rate derivatives products are typically private, customized contracts between two financial institutions or between a financial institution and one of its clients.

The Nature of Futures Trading and the Role of the Clearinghouse

Futures Positions

A speculator or hedger can take one of two positions on a futures (or forward) contract: a long position (or futures purchase) or a short position (futures sale). In a long futures position, one agrees to buy the contract’s underlying asset at a specified price, with the payment and delivery to occur on the expiration date (also referred to as the delivery date). In a short position, one agrees to sell an asset at a specific price, with delivery and payment occurring at expiration.

To illustrate how positions are taken, suppose in December, Speculator X believes that summer will be unusually dry in the Midwest, resulting in increases in the price of corn. With hopes of profiting from this expectation, suppose on 12/14/15 Speculator X decides to take a long position in a July corn futures contract and instructs her broker to buy one July corn futures contract listed on the CBT (one contract is for 5,000 bushels, see Exhibit 1.2). To fulfill this order, suppose X’s broker finds a broker representing Speculator Y, who believes that the summer corn harvest will be above normal and therefore hopes to profit by taking a short position in the July corn contract. After negotiating with each other, suppose the brokers agree to a price of $3.89/bu. on the July contract for their clients. In terms of futures positions, Speculator X would have a long position in which she agrees to buy 5,000 bushels of corn at $3.89/bu. from Speculator Y at the delivery date in July, and Speculator Y would have a short position in which he agrees to sell 5,000 bushels of corn at $3.89/bu. at the delivery date in September.

EXHIBIT 1.2 Bloomberg Spot and Futures Corn Prices

If both parties hold their contracts to delivery, their profits or losses would be determined by the price of corn on the spot market (also called cash, physical, or actual market). For example, suppose the summer turns out to be mild, causing the spot price of corn to trade at $3.32/bu. at the grain elevators in the Midwest at or near the delivery date on the July corn futures contract. Accordingly, Speculator Y with his short position would buy the corn on the spot market for $3.32/bu, and then sell it on the futures contract to Speculator X for $3.89/bu., resulting in a $2,850 profit minus commission and transportation costs. Speculator X with her long position, in turn, would have to buy 5,000 bushels of corn on her corn futures contract at $3.89/bu. from Speculator Y, and then sell the corn for $3.32/bu. on the spot market, losing $2,850 plus commission and transportation costs.

Clearinghouse

To provide contracts with marketability, futures exchanges use clearinghouses. The clearinghouses associated with futures exchanges guarantee each contract and act as intermediaries by breaking up each contract after the trade has taken place. Thus, in the previous example, the clearinghouse (CH) would come in after Speculators X and Y have reached an agreement on the price of the July corn, becoming the effective seller on X’s long position and the effective buyer on Y’s short position. Once the clearinghouse has broken up the contracts, then X’s and Y’s contracts would be with the clearinghouse. The clearinghouse, in turn, would record the following entries in its computers:

Clearinghouse Record:

1. 2.

Speculator X agrees to buy July corn at $3.89/bu. from the clearinghouse. Speculator Y agrees to sell July corn at $3.89/bu. to the clearinghouse.

This intermediary role of the clearinghouse makes it easier for futures traders to close their positions before expiration. Returning to our example, suppose that early summer is dry in the Midwest, leading a third speculator, Speculator Z, to want to take a long position in the listed July corn futures contract. Seeing a profit opportunity from the greater demand for long positions in the July contract, suppose in June Speculator X agrees to sell a July corn futures contract to Speculator Z for $4.14/bu. Upon doing this, Speculator X now would be short in the new July contract, with Speculator Z having a long position, and there now would be two contracts on July corn. After the new contract between X and Z has been established, the clearinghouse would step in and break it up. For Speculator X, the clearinghouse’s record would now show the following:

Clearinghouse Record for X:

1. 2. Close

Speculator X agrees to buy July corn at $3.89/bu. from the clearinghouse. Speculator X agrees to sell July corn at $4.14/bu. to the clearinghouse. Thus, to close, the Clearinghouse owes X $0.25 per contract to be paid at expiration: ($0.25/bu.)(5,000 bu.) = $1,250.

The clearinghouse accordingly would close Speculator X’s positions by paying her $0.25/bu. ($4.14/bu. − $3.89/bu.), a total of $1,250 on the contract [(5,000 bu.)($0.25/bu.)]. Since Speculator X’s short position effectively closes her long position, it is variously referred to as a closing, reversing out, or offsetting position or simply as an offset. Thus, the clearinghouse makes it easier for futures contracts to be closed prior to expiration.

Commission costs and the costs of transporting commodities cause most futures traders to close their positions instead of taking delivery. As the delivery date approaches the number of outstanding contracts, known as open interest, declines, with only a relatively few contracts still outstanding at delivery. Moreover, at expiration, the contract prices on futures contracts established on that date (fT) should be equal (or approximately equal) to the prevailing spot price on the underlying asset (ST). That is, at expiration: fT = ST. If fT does not equal ST at expiration, an arbitrage opportunity would exist. Arbitrageurs could take a position in the futures contract and an opposite position in the spot market. For example, if the July corn futures contract were available at $3.25 on the delivery date in July and the spot price for corn were $3.32 at a grain elevator near the delivery place specified on the contract (resulting in no hauling cost), then arbitrageurs could go long in the July contract, take delivery by buying the corn at $3.25 on the futures contract, and then sell the corn on the spot at $3.32 to earn a riskless profit of $0.07/bu. Arbitrageurs’ efforts to take long positions, however, would drive the contract price up to $3.32. On the other hand, if fT exceeds $3.32, then arbitrageurs would reverse their strategy, pushing fT to $3.32/bu. Thus, at delivery, arbitrageurs will ensure that the prices on expiring contracts are equal to the spot price or the spot prices plus the hauling cost. As a result, closing a futures contract with an offsetting position at expiration will yield the same profits or losses as closing futures positions on the spot by purchasing (selling) the asset on the spot and selling (buying) it on the futures contract.

Returning to our example, suppose that near the delivery date on the July contract, the spot price of corn and the price on the expiring corn futures contracts are $3.63/bu. To close his existing short contract, Speculator Y would need to take a long position in the July contract, while to offset her long contract, Speculator Z would need to take a short position. Suppose Speculators Y and Z take their offsetting positions with each other on the expiring July corn contract priced at fT = ST