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- Herausgeber: John Wiley & Sons
- Kategorie: Fachliteratur
- Serie: Wiley Finance Editions
- Sprache: Englisch
SOFR Futures and Options is the practical guide through the maze of the transition from LIBOR. In the first section, it provides an in-depth explanation of the concepts involved: * The repo market and the construction of SOFR * SOFR-based lending markets and the term rate * The secured-unsecured basis * SOFR futures and options and their spread contracts * Margin and convexity Applying these insights, the second section offers detailed worked-through examples of hedging loans, swaps, bonds, and floors with SOFR futures and options, supported by interactive spreadsheets accessible on the web. The gold standard resource for professionals working at financial institutions, SOFR Futures and Options also belongs in the libraries of students of finance and business, as well as those preparing for the Chartered Financial Analyst exam.
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Veröffentlichungsjahr: 2022
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Table of Contents
Cover
Title Page
Copyright
Foreword
A LITTLE BIT OF HISTORY
A REVOLUTION IN FINANCE
ALL THE BEST
Introduction
EURODOLLARS
EURODOLLAR FUTURES
LIBOR
THE GREAT FINANCIAL CRISIS
THE LIBOR RIGGING SCANDAL
SOFR AND REPO MARKETS
SOFR FUTURES AND OPTIONS: TOPICS AND STRUCTURE OF THIS BOOK
IMPLICATIONS OF SOFR FOR MARKET ANALYSIS
REMAINING HURDLES IN THE TRANSITION FROM LIBOR TO SOFR
THE TRANSITION CONTINUES
NOTES
SECTION ONE: Concepts
CHAPTER 1: SOFR
THE REPO MARKET
SOFR: DEFINITIONS AND FEATURES
CALCULATING A REFERENCE REPO RATE
ORIGIN OF REPO RATES USED FOR SOFR CALCULATION
SOFR VERSUS FED FUNDS
SOFR SPIKES AND THE SRF
BENEFITS AND (POTENTIAL) PROBLEMS OF SOFR
NOTES
CHAPTER 2: SOFR Futures
3M SOFR FUTURES: CONVENTIONS
3M SOFR FUTURES AS MARKET PRICES FOR CONSECUTIVE 3M FORWARD SOFR
3M SOFR FUTURES: STRIPS
3M SOFR FUTURES: ROLLS
1M SOFR FUTURES: CONVENTIONS
1M VERSUS 3M SOFR FUTURES
1M AND 3M SOFR FUTURES: LIQUIDITY
1M AND 3M SOFR FUTURES: ASSESSING THE EFFECT OF FOMC MEETINGS
PRICING AND HEDGING WITH SOFR FUTURES: GENERAL CONSIDERATIONS
EFFECT OF PROCESS SELECTION ON THE PRICING OF SOFR FUTURES
EXAMPLE FOR HEDGING A SOFR TERM RATE WITH SOFR FUTURES VIA A JUMP PROCESS
NOTES
CHAPTER 3: SOFR Lending Markets and the Term Rate
CONVENTIONS OF SOFR-BASED LENDING MARKETS
STATUS OF SOFR-BASED LENDING MARKETS
SIMPLE AVERAGING VERSUS DAILY COMPOUNDING
THE SOFR INDEX
TERM RATE
THE MODEL TRANSLATING SOFR FUTURE PRICES IN SOFR TERM RATES
CRITICISM OF THE CME TERM RATE
TWO SCENARIOS FOR THE FURTHER EVOLUTION OF THE TENSION AND HENCE THE TERM RATE
NOTES
CHAPTER 4: SOFR Spread Futures and the Basis
SOFR FUTURES IN THE STIR UNIVERSE
DRIVING FORCES OF SPREADS IN THE STIR UNIVERSE
CME'S SPREAD CONTRACTS
DRIVING FACTORS OF THE SECURED–UNSECURED BASIS
A MODEL FOR THE SECURED–UNSECURED BASIS, LINKING IT WITH OTHER BASES (CCBS)
FIRST APPLICATION OF THIS MODEL: PRICING SPREAD FUTURES
SECOND APPLICATION OF THIS MODEL: REPLACING THE CCBS WITH SPREAD FUTURES IN SOME RV TRADES
THIRD APPLICATION OF THIS MODEL: NEW RV RELATIONSHIP
THE CCBS AND THE MODEL AFTER THE END OF LIBOR
REMAINING PRODUCTS WITH EXPOSURE TO THE BASIS AFTER THE END OF LIBOR
SWAPS WITH SOFR AS FLOATING LEG AND ASSET SWAPS AFTER THE END OF LIBOR
HEDGING SOFR-BASED SWAPS AND GOVERNMENT BONDS WITH SOFR FUTURES
NOTES
CHAPTER 5: SOFR Future Options
OPTIONS ON 3M SOFR FUTURES: PRODUCT SUITE AND SPECIFICATIONS
OVERVIEW OF GENERAL VOLATILITY ANALYSIS
DISTRIBUTION OF REALIZED VOLATILITY OVER THE SECURED YIELD CURVE
CURRENT IMPLIED VERSUS HISTORICAL REALIZED VOLATILITY
OPTIONS ON SOFR FUTURES VERSUS OPTIONS ON ED FUTURES
OPTIONS ON 1M SOFR FUTURES: PRODUCT SUITE AND SPECIFICATIONS
OVERVIEW OF AVAILABLE PRICING MODELS FOR ASIAN OPTIONS
A POSSIBLE ROAD MAP TOWARD PRICING OPTIONS ON SOFR FUTURES DURING THE REFERENCE PERIOD
IMPACT OF PROCESS SELECTION ON THE PRICING OF OPTIONS ON SOFR FUTURES
NOTES
CHAPTER 6: Pricing Biases and SOFR Curve Building
BIASES IN EURODOLLAR FUTURES PRICES
NONLINEARITIES RESULTING FROM CONTRACT DEFINITIONS
BIASES IN SOFR FUTURES
BUILDING A SOFR SWAP CURVE FROM SOFR FUTURES
NOTE
SECTION TWO: Use Cases
CHAPTER 7: Simple Examples of Hedging with SOFR Futures
EXAMPLE 1: CORPORATE TREASURER CONVERTING FLOATING RATE EXPOSURE TO FIXED
EXAMPLE 2: LOCKING IN AN INTEREST RATE WITH MISMATCHED DATES
EXAMPLE 3: USING ONE-MONTH SOFR FUTURES AS A HEDGING ALTERNATIVE
LESSONS TO BE LEARNED FROM THESE THREE SIMPLE EXAMPLES
NOTES
CHAPTER 8: Hedging the CME Term SOFR Rate
THE TERM SOFR METHODOLOGY
THE CME TERM SOFR OBJECTIVE FUNCTION
OBTAINING FUTURES PRICES TO USE AS INPUTS TO THE TERM SOFR MODEL
HEDGING TERM SOFR EXPOSURE
A PRECISE APPROACH TO HEDGING CME TERM SOFR EXPOSURE
PRACTICAL CONSIDERATIONS
NOTES
CHAPTER 9: Hedging Swaps and Bonds with SOFR Futures
TREASURIES VERSUS SOFR FUTURES STRIPS
HEDGING SOFR SWAPS WITH SOFR FUTURES
HEDGING TREASURIES WITH SOFR FUTURES
NOTES
CHAPTER 10: Hedging Caps and Floors with SOFR Futures Options
HEDGING WITH OPTIONS ON 3M SOFR FUTURES BEFORE THEIR REFERENCE QUARTER STARTS
MANAGING THE HEDGE DURING THE REFERENCE QUARTER
BASIC REPLICATION STRATEGIES OF CAPS AND FLOORS WITH 1M FUTURE OPTIONS
DEALING WITH DAILY FLOORS
NOTES
Bibliography
Index
End User License Agreement
List of Tables
Chapter 2
TABLE 2.1 Fair value of Sep 2022 SR1–SR3 spread
TABLE 2.2 Simulated average settlement price of the Mar 2022 SR3 future
TABLE 2.3 Simulated average settlement price of the Mar 2022 SR3 future usin...
Chapter 3
TABLE 3.1 Conventions for loans in-arrears until (day)
T
TABLE 3.2 Compound term rate for a loan from 3 Jan 2022 to 3 Jan 2023
Chapter 4
TABLE 4.1 Spread contracts between CME's STIR futures
TABLE 4.2 Multiple regression of the SR3:ED future spread versus SOFR and 2Y...
TABLE 4.3 Model prediction of the SR3:ED future spread
TABLE 4.4 Mean reversion characteristics of the residuals from Figures 4.6 a...
Chapter 5
TABLE 5.1 Realized volatility in different parts of the secured rate curve o...
TABLE 5.2 Simulated average payoff of a call on the Mar 2022 SR3 future with...
Chapter 6
TABLE 6.1 SOFR futures prices as of 25-Feb-22
Chapter 7
TABLE 7.1 Fitting a stepwise rate curve to one-month SOFR futures prices
TABLE 7.2 Calculations for a hedge of a simple deposit using one-month SOFR ...
Chapter 8
TABLE 8.1 Calculations for hedge of 3M term SOFR starting 27-Apr-22, as of 2...
Chapter 9
TABLE 9.1 Evolution of a hedge of a Treasury note with a SOFR futures strip...
Chapter 10
TABLE 10.1 Simulated premium of daily versus compound caps in %
List of Illustrations
Chapter 1
FIGURE 1.2 SOFR: Segments of the repo market used as data input for SOFR cal...
FIGURE 1.4 Volume in different sectors of the repo market
FIGURE 1.5 Difference of rates associated with percentiles
FIGURE 1.6 Difference of rates associated with percentiles
FIGURE 1.7 Mean and standard deviation of a normal distribution fitted to th...
FIGURE 1.8 Histogram of observed standard deviations
FIGURE 1.9 SOFR versus EFFR
FIGURE 1.10 SOFR versus EFFR
FIGURE 1.11 SOFR rate and volume of repo transactions used for SOFR calculat...
Chapter 2
FIGURE 2.1 The aggregation of daily SOFR via the future before the reference...
FIGURE 2.4 SOFR futures during reference quarter
FIGURE 2.5 SOFR future price history
FIGURE 2.6 Consecutive 3M forward rates of the secured yield curve as implie...
FIGURE 2.7 Consecutive 3M forward rates of the secured yield curve as implie...
FIGURE 2.8 Calculating strip rates from ED and SR3 futures
FIGURE 2.9 Rolls for past 3M SOFR futures
FIGURE 2.12 Time periods covered by 1M and 3M SOFR futures
FIGURE 2.14 SOFR future daily volume
FIGURE 2.15 SOFR future open interest
FIGURE 2.16 FOMC meeting dates relative to the reference periods of 1M and 3...
FIGURE 2.17 Different functional forms for the forward SOFR curve
FIGURE 2.18 SOFR (proxy) as modeled by an Ornstein-Uhlenbeck process
FIGURE 2.19 Futures as a hedge via calibrating a process
Chapter 3
FIGURE 3.1 SOFR issuance by quarter
FIGURE 3.3 SOFR term rates: calculation process
Chapter 4
FIGURE 4.1 Relationship between CME's STIR futures
FIGURE 4.2 Volume of spread contracts during 2021
FIGURE 4.3 EFFR minus SOFR
FIGURE 4.4 Regression of SR3:ED spread versus 2Y JPY CCBS
FIGURE 4.5 Actual versus modeled SR3:ED spread
FIGURE 4.6 Regression residuals of the SR3:ED spread versus 2Y JPY CCBS
FIGURE 4.7 Regression residuals of the SR3:ED spread versus SOFR and 2Y JPY ...
FIGURE 4.8 Relationship between floating legs of swaps
Chapter 5
FIGURE 5.3 Options on SR3 futures
FIGURE 5.4 Realized volatility (normal in bp, annualized) of the secured rat...
FIGURE 5.5 Realized volatility (normal in bp, annualized) of the secured rat...
FIGURE 5.6 Average Sharpe ratios for the SOFR future curve
FIGURE 5.7 “Current” implied versus historical realized volatility along the...
FIGURE 5.8 Realized volatility (normal in bp, annualized) of the Jun 2022 ED...
Chapter 6
FIGURE 6.1 Time
T
values of all-in interest earned via futures and FRA hedge...
FIGURE 6.2 Fitted curve pricing errors for first 13 one-month SOFR futures c...
FIGURE 6.3 Fitted curve pricing errors for first 17 three-month SOFR futures...
FIGURE 6.4 Fitted SOFR curve
FIGURE 6.5 Fitted SOFR curve with regularity condition
Chapter 7
FIGURE 7.1 SOFR
FIGURE 7.2 Actual and implied SOFR values
FIGURE 7.3 Intended lending period and period covered by Dec-19 3M SOFR futu...
FIGURE 7.4 Fitted stepwise overnight SOFR curve
FIGURE 7.5 Fitted stepwise overnight SOFR curve and actual realized SOFR val...
Chapter 8
FIGURE 8.1 6M term SOFR rate as a function of λ for 27-Jan-22
Chapter 9
FIGURE 9.1 Integration of SOFR into a term rate in the future, swap, and Tre...
FIGURE 9.2 CMT minus future strip yields
FIGURE 9.3 Date mismatches between the hegded instrument and the SOFR future...
FIGURE 9.4 Evolution of the Treasury and of the hedging futures portfolio...
Chapter 10
FIGURE 10.1 The aggregation of daily SOFR via the future before the referenc...
FIGURE 10.2 Implied strikes for obtaining a 1.8% and a 1.9% floor during Jun...
FIGURE 10.3 Underlying of SOFR-based floors and options on 3M SOFR futures...
Guide
Cover
Table of Contents
Title Page
Copyright
Foreword
Introduction
Begin Reading
Bibliography
Index
End User License Agreement
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SOFR Futures and Options
A Practitioner’s Guide
DOUG HUGGINS
CHRISTIAN SCHALLER
Copyright © 2022 by Doug Huggins and Christian Schaller. All rights reserved.
Published by John Wiley & Sons, Inc., Hoboken, New Jersey.Published simultaneously in Canada.
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Foreword
by Galen Burghardt
February 2022
Writing this foreword is a little like writing an obituary for a dear friend. LIBOR, and the Eurodollar futures and options contracts that have been tied to it for nearly 40 years, will be put to bed soon. And so ends a remarkable era of financial innovation that transformed the world of interest rate risk management and academic research.
Still, if you're reading this Foreword, chances are that SOFR, and its related futures and options contracts, have made the competitive cut and are serving as replacements for my old friends. So let's spend the next few paragraphs reflecting on what we've learned.
I think I can be most helpful by recounting some of the reasons the Eurodollar futures contract helped to revolutionize the world of banking and finance. And by finance, I mean both applied and academic.
A LITTLE BIT OF HISTORY
First, it's worth remembering that at the time Eurodollar futures were first listed in the 1980s, there had never been a futures contract that cash settled to an abstract concept. In talking with Rick Kilcollin, who was largely responsible for the contract's design, I learned that the LIBOR market in the early 1980s was thin, and that the development of an index that could capture a relevant financing rate and resist attempts at manipulation was still unfinished. With that in mind, what the Chicago Mercantile Exchange (CME) devised was an ingenious survey in which banks of whatever credit rating were not asked what rate they were paying for interbank funds in London. Instead, they were asked to provide the rate at which they perceived funds were offered to prime quality banks. This, combined with the practice of throwing out the high and low responses, produced a survey outcome with an astonishing degree of agreement.
Second, it's worth remembering that when the contracts were first listed, they were the runty cousins of the certificate of deposit contract. A special, and less expensive, membership was created by the CME for trading the contract, which took place in a small corner of the CD pit. I may have made up this story, but I recall someone saying that Fred Arditti, who was the CME's head of research at the time, would visit the pit each day and come back saying, “I die a little each day when I see how little is going on there.”
Then all hell broke loose. Continental Illinois, whose CDs were deliverable into the CD futures contract (and whose motto was “We will find a way”) suffered some substantial loan losses and took a hit to its credit rating. It didn't take long for the market to start worrying about credit risk in the deliverable instrument and to look elsewhere.
At the same time, the interest rate swaps market was beginning to take hold and grow, and the Eurodollar futures market was poised perfectly to go along for the ride.
A REVOLUTION IN FINANCE
Eurodollar futures proved to be a financial engineer's dream tool. In the 1980s, the idea of zero-coupon bonds was largely found in textbooks. As was the idea that one could break up the yield curve into three-month (3M) segments and use those segments to study yield curve behavior and the sensitivity of one's financial position to each of those segments.
Now these ideas seem commonplace, but at the time, the world of bonds was almost unbelievably primitive – at least in the world of actual bonds. And the market for forward rates was nearly nonexistent. Try to imagine, for example, what it was like to extract a continuously compounded forward rate curve from the traded bond market. Even if one used data from the Treasury market – possibly the deepest and most liquid bond market in the world – the results could be almost hilariously erratic. In contrast, with Eurodollar futures, one had the next best thing – a quarterly compounded forward rate curve – served on a platter.
Well, almost. It's one thing to know that convexity matters, and another to know just how much. In the late 1980s, Terry Belton and I published a piece for our clients at Discount Corporation of New York Futures called The Financing Bias in Eurodollar Futures. The idea was a simple one based on the daily settlement of gains and losses on futures. That is, if one were short Eurodollar futures, one would be able to invest cash coming in at higher rates (i.e., when rates were going up and you were making money on your short position) and borrow the cash you paid out at lower rates when rates were falling. This was an obvious advantage to the shorts, and if you could do it long enough and over big enough swings, the advantage could add up to real money. At the time we published the note, though, the Eurodollar futures curve only went out a year or two, and the advantage proved not to be worth much for such short-dated contracts. So that research note sank without a trace.
In time, though, the CME extended the Eurodollar futures curve out to 5 years and then to 10 years. And when it did, the interest rate swaps market used these newly available futures rates to price their swaps. The problem, though, as Bill Hoskins and I discovered when we published The Convexity Bias in Eurodollar Futures – perhaps one of the most important research notes of our working lives – was that the market had failed to take the value of convexity into account. Swaps were priced as if futures rates were forward rates so that it was possible to receive fixed on a swap and hedge the position by shorting Eurodollar futures and make completely riskless money as rates rose and fell. Not long after we published that note, the market became aware of the mispricing and completely readjusted.
Another lesson that Bill Hoskins taught me, although it took him a while, was that forward rates (or prices) are breakeven values. That is, if you finance a position to any given forward date, you know just how much the price of what you have can rise or fall before you make or lose money as of that forward date. This is a hugely valuable tool.
One example of just how valuable a tool it is came when Gavin Gilbert, a wonderfully voluble friend of mine, rang me one day to announce, more or less at the top of his lungs, “Galen! You won't believe it! I just bought the forward 2-year TED for zero!” For this to make sense, you need to know that we had just published a good piece of work called Measuring and Trading Term TED Spreads. This was the basis for much of what you could find on Bloomberg if you visited that particular page. We had not, however, considered the buying and selling of term TEDs forward. But Gavin had. He found that if he bought a two-year note two months forward and sold the appropriate strip of Eurodollar futures, he basically owned the spread at 0. Since the two-year TED spread at the time was trading at roughly 20 basis points, he expected to make 20 basis points on the trade. And he also knew that the spread would have to go negative for him to lose money.
I, of course, checked into it and found that by the time I got there, the spread could be bought forward for 10 basis points. So we published a note (as Gavin knew we would) telling our clients about the trade. What made the trade remarkable, though, was that even with highly sophisticated and integrated markets, the term repo market was not yet in sync with the term LIBOR market. Hence the glaring mispricing.
One of the things you learn in any class on derivatives is that the gains and losses on the derivative look just like the gains and losses you would experience on a trade that you could construct in the cash market. So, for example, a long Eurodollar futures position has the same payoff as a cash position in which you borrow money for a term equal to the contract's expiration date and lend for a term that is three months longer. As a result, a long Eurodollar futures position is the equivalent of a simple borrow short/lend long yield curve trade.
Once, during one of our classes on Eurodollar futures, a young man from Panagora asked me what the Sharpe ratio of a Eurodollar contract would look like. It was the first time I'd ever heard the question, so I had to beg off. But when we got back to the office, we tackled the question and found that we could analyze the gains and losses combined with their standard deviations and calculate very straightforward Sharpe ratios. When we did this, we learned that the most profitable part of the yield curve carry trade was in the first two or three years of the yield curve. If you're interested, you can find these early results on page 64 of The Eurodollar Futures and Options Handbook, at least until it disappears from the face of the earth. Or you can look for one of our yield curve carry notes such as Yield Curve Carry Rides Again.
It was neat, too, that these results conformed to what Antti Ilmanen had written in one of his extraordinary monographs at Salomon Brothers. The note was called Does Duration Extension Enhance Long-Term Expected Returns? (Ilmanen 1995). He concluded that once you got past the two-year mark, you had more or less exhausted any useful excess returns and that no, you didn't get paid for taking extension risk.
I should add that one of the greatest contributions of Eurodollar futures in the banking industry can be attributed to one of its most prosaic features. That is, they were futures contracts, which meant that one could buy them in the morning and sell them in the afternoon and have the positions offset. For asset/liability managers, this feature was a godsend. The chairman of JPMorgan's asset/liability committee once volunteered in casual conversation that they had revolutionized his life. He was no longer bound to deposit, swap, and forward rate agreement positions that would stay on the books for weeks, months, or years (and that carried with them all kinds of credit risk). Instead, if his bank's risk position changed during the course of a trading day, he could simply add to or offset open futures positions without having to worry about being stuck with them.
ALL THE BEST
To conclude, before I wear out my welcome here, I would like to thank Doug and Christian for inviting me to contribute this Foreword. It gave me a chance to think back over some of the great joys of being in these markets at a time when financial history was being made and to reconnect with some old friends. I would also like to thank my colleagues at the CME for all the support they have given me over the years. The time I spent there from 1983 to 1986 were great fun and set me up for a career that I could never have imagined. And, of course, the CME's financial support for The Eurodollar Futures and Options Handbook made it possible to produce a volume that has been paying dividends for nearly 20 years.
So, with that, thank you all. And let's hope that the next 40 years of trading and innovation are just as thrilling as the past 40 years have been. Or as my old boss and mentor, Morton Lane, liked to say, “May we all have prosperous futures with many options.”
Galen Burghardt
Evanston, IL
February, 2022
Introduction
This book is about the SOFR futures and options complex at the Chicago Mercantile Exchange (CME). Before providing an overview of its topics, we take a look at the relevant history. To understand SOFR futures and options, we need to understand SOFR; to understand SOFR, we need to understand LIBOR; and to understand LIBOR, we need to understand Eurodollars.
EURODOLLARS
The most basic definition of a Eurodollar is a US dollar held in a bank outside of the United States. Given that dollars are fungible, it may not be obvious that a dollar held offshore should differ in any respect from a dollar held onshore. But depository institutions in jurisdictions other than the United States are subject to different regulations than those in the United States. For example, the US government is typically unable to confiscate assets held by banks domiciled outside of the United States. And this fact figures prominently in some of the origin stories of the Eurodollar market.
One such story is that the Chinese government, fearing confiscation of its dollar balances after the outbreak of the Korean War in 1950, transferred most of these balances to Banque Commerciale pour l'Europe du Nord, a Paris-based bank that had been started by Russian exiles in 1921 and acquired by Gosbank in 1925 (Dormael 1997, pp. 1–9). These offshore dollars, opened in the name of the Hungarian National Bank, became the first Eurodollars. They were later leant to various French banks and to the Paris branch of Bank of America. Over time, other communist countries channeled their dollars through Europe, with the business expanding to another Russian institution, the Moscow Narodny Bank, based in London. These offshore dollars were leant to various Western European governments, and by the late 1950s, American multinationals were using funds obtained in this market to finance their expansion throughout Europe.
Another feature of the Eurodollar market was that these offshore dollars were not subject to the typical exchange rate controls that governed onshore deposits. For example, in 1955, Midland Bank found it profitable to acquire 30-day offshore dollar deposits at a rate of 1.875% for the purpose of buying sterling in the spot market and selling it 30 days forward at a premium of 2.125%. In this FX swap, Midland paid an effective rate of 4% for pounds sterling at a time when the official rate at the Bank of England was 4.5%. The rate Midland paid for these offshore dollars was well above the maximum rate of 1% for 30-day deposits specified at the time by Regulation Q in the United States. But exchange controls prevented the arbitrage using onshore dollars. By tapping the Eurodollar market, Midland was able to pursue the arbitrage despite exchange rate controls – and despite the interest rate premium paid in the offshore market.
Eurodollars include other benefits as well. For example, they don't attract an FDIC insurance fee, estimated currently to be on the order of 8 to 9 basis points for large banks (Keating and Macchiavelli 2017). And they aren't subject to central bank reserve requirements. So while dollars are fungible in a broad sense, dollars can sometimes be put to a wider variety of uses when they're held overseas.
EURODOLLAR FUTURES
As the market matured, various futures exchanges considered the possibility of introducing futures contracts on Eurodollars. At one point, the Chicago Mercantile Exchange considered a futures contract that required the seller to open an offshore time deposit for the buyer. But this procedure was considered too cumbersome, so the CME designed the contract to be cash-settled. No other futures contract had settled with a simple cash payment at expiration, so the CME was taking a bit of a risk with this contract (Burghardt 2003).
In order for the contract to be settled in cash, the CME needed a way to construct an index to be used in calculating the final settlement price of the contract. To that end, the CME designed an interesting process. Each day, it would randomly select 20 banks from a pool of London banks active in the Eurodollar market and ask each bank for the rate at which it believed prime quality banks could borrow dollars for three months. The highest and lowest quartiles were discarded, and the two middle quartiles were averaged. Then, at some randomly chosen time during the subsequent 90 minutes, the process was repeated with a second set of randomly chosen banks. The CME then averaged the two results (Robb 2012).
It's important to note that the CME did not publish the identities of the banks that participated in either of the two surveys.
This system worked well for quite some time. But in 1996, the reference rate for Eurodollar contracts was no longer the dominant index for the massive market over-the-counter interest rate swaps, and CME applied for permission to switch from the reference rate it had been calculating since 1981 to LIBOR.
LIBOR
In the early 1980s, the market had a need for standardized reference rates that could be used to settle various forms of interest rate swaps, and members of the British Bankers Association (BBA) asked the BBA to arrange a standardized interest rate for this purpose. In 1984, the BBA introduced the BBAIRS code – the British Bankers Association Interest Rate Swap code. This code suggested terms and conditions to govern interbank transactions with maturities up to two years. And as part of this process, the BBA in 1984 introduced BBA interest settlement rates. The rate-setting process continued to evolve and was standardized by the BBA in 1986 as LIBOR – the London Interbank Offered Rate.
The LIBOR rate determination process was similar in spirit to the process the CME had used since 1981 for its Eurodollar futures contract. But there were a few differences. For example, the BBA polled the same 16 banks every day. And since the same banks were polled each day, there was no need to poll them a second time during the day. And, unlike the CME, the BBA publicly displayed the rate submitted by each bank in the panel.
The fact that the rate submitted by each bank was made public mattered even more when, in 1998, the question submitted to each bank was changed. The original question was, “At what rate do you think interbank term deposits will be offered by one prime bank to another prime bank for a reasonable market size today at 11 a.m.?” The new question was changed to read, “At what rate could you borrow funds, were you to do so by asking for and then accepting interbank offers in a reasonable market size just prior to 11 a.m.?” [Emphasis added.]
And it was this new question to which banks were responding when the Great Financial Crisis of 2008 hit.
THE GREAT FINANCIAL CRISIS
The subprime mortgage crisis, which started in 2007, eventually led to a number of bank failures in 2008. The most notorious examples were Bear Stearns in March of that year and Lehman Brothers in September, but the entire banking system was deeply affected, and the Federal Reserve orchestrated a large-scale infusion of capital into the banking system, largely via the purchase of preferred shares in 42 US banks. Similar assistance was provided in one form or another to banks in many other jurisdictions, including the UK and many other parts of Europe.
One of the consequences of the great financial crisis is that banks largely stopped lending to one another on an unsecured basis, as each bank was unsure about the creditworthiness of the others. Central banks quickly stepped into the breach, providing substantial funding via repo operations and collateralized currency swap lines with other central banks.
With unsecured interbank lending greatly reduced, the LIBOR polling process became somewhat academic. How would a bank know where it could borrow in the interbank market if it wasn't active in the interbank market? And if no banks were active in the interbank market, what was the LIBOR polling process measuring precisely?
Perhaps Citigroup's Willem Buiter put it best when he said, “LIBOR is the rate at which banks don't lend to one another.” Questioned about this comment in a Parliamentary committee hearing, Bank of England Governor Mervyn King commented:
The world has changed totally; people are very worried about lending, and indeed hardly anybody is willing to lend to any bank around the world for three months unsecured; they want to lend secured.… I think that in future we will see far less lending to banks on an unsecured basis and far more on a secured basis. The inter-bank market has very often been a market in which overnight or short-term cash holdings can be distributed around the banking system, and banks were willing to do it with each other unsecured at Libor. I just do not think it plays that role now, and I think we are going to see developing over the next few years a much more intensive method in which banks can redistribute cash surpluses and shortages among each other on a more secured basis. At present they are doing it directly with the central bank, and that is true around the world, not just in the UK.1
THE LIBOR RIGGING SCANDAL
If LIBOR's days were numbered as a result of the switch from unsecured to secured interbank lending, the nail in the coffin was evidence that the process had been manipulated by some of the traders at some of the banks in the LIBOR survey panel.
As early as April 2008, the Wall Street Journal published an article suggesting some banks were submitting LIBOR rates that were unjustifiably low (Mollenkamp 2008). Two reasons were offered for this behavior. First, some of these banks – and their clients – stood to gain if the published LIBOR rates could be suppressed. Second, some of these traders hoped to give the appearance that all was well with their particular bank. For example, it came out in hearings that Paul Tucker, then executive director of markets at the Bank of England, had called Barclay's CEO, Bob Diamond, regarding Barclay's LIBOR submissions. Diamond's notes from that call are quite revealing:
Further to our last call, Mr Tucker reiterated that he had received calls from a number of senior figures within Whitehall to question why Barclays was always toward the top end of the Libor pricing. His response was, “You have to pay what you have to pay.” I asked if he could relay the reality, that not all banks were providing quotes at the levels that represented real transactions; his response: “Oh, that would be worse.”
I explained again our market rate driven policy and that it had recently meant that we appeared in the top quartile and on occasion the top decile of the pricing. Equally I noted that we continued to see others in the market posting rates at levels that were not representative of where they would actually undertake business. This latter point has on occasion pushed us higher than would otherwise appear to be the case. In fact, we are not having to “pay up” for money at all.
Mr. Tucker stated the level of calls he was receiving from Whitehall were “senior” and that while he was certain we did not need advice, that it did not always need to be the case that we appeared as high as we have recently. (House of Commons 2012).2
In the end, a slew of bankers were convicted for their roles in the LIBOR rigging scandal, and fines totaling more than USD 9 billion were levied against large banks, including Barclays, Citigroup, Deutsche Bank, JP Morgan, Lloyds, RBS, Rabobank, and UBS.
Perhaps most significant for our purposes is that regulators in many jurisdictions concluded that LIBOR was not fit for purpose and that it needed to be retired. In different parts of the world, authorities have suggested different candidates for replacing LIBOR. But in the US, authorities have settled on SOFR – the secured overnight financing rate.
SOFR AND REPO MARKETS
To understand SOFR, one needs first to understand repo – short for repurchase agreement. As the name suggests, a repo transaction is one in which a security – typically a bond – is sold and simultaneously repurchased at an agreed price with settlement on an agreed date in the future. In other words, the bond is sold in the spot market and simultaneously bought back on a forward date for a different price. The repurchase price is typically greater than the sale price, and the difference between the two prices reflects the cost of borrowing between the sale date and the subsequent repurchase date, with the bond serving as collateral.
For example, imagine that I could sell USD 100 million par amount of bonds for an invoice price3 of 101,000,000 in the spot market and that I simultaneously could arrange to repurchase those same bonds tomorrow for an invoice price of USD 101,000,280.56. The difference between the sale price and the purchase price – USD 280.56 in this case – is the interest I pay to borrow USD 101 million overnight. In this example, the overnight repo rate is (280.56 / 101,000,000) × (360/1) = 0.001 – i.e., 0.1%.
The mechanics of this repo transaction involve me selling a bond today and simultaneously agreeing to repurchase the bond tomorrow at a price we agree on today. But the economic rationale for repo transactions is to borrow money using a bond as collateral for the loan – i.e., to arrange a secured financing – in this case, an overnight secured financing. Not surprisingly, the repo rate associated with this overnight secured financing is called the secured overnight financing rate (SOFR). We describe the mechanics of the repo market and the secured overnight financing rate in much greater detail in Chapter 1.
As it happens, the repo market is a very large, very active market. The Brookings Institution estimated the average daily turnover in the US repo market in 2021 at somewhere between USD 2 trillion and USD 4 trillion per day. Repo agreements can be arranged for various terms, but the most common term is one day – i.e., overnight. In fact, even when people intend to borrow funds for a longer period, they often simply arrange to leave the repo agreement “open,” meaning the repo arrangement will keep rolling over for a term of one day until otherwise ended by one of the two parties to the transaction.
Many large institutions are required to report repo transactions, with the result that the Federal Reserve has a wealth of daily repo transactions that it can use to monitor the market for overnight secured financing.4
With LIBOR viewed as an unreliable benchmark, the Board of Governors of the Federal Reserve and the Federal Reserve Bank of New York in 2014 jointly convened the Alternative Reference Rate Committee (ARRC) for the purpose of identifying a risk-free replacement for USD LIBOR. Over time, the membership of ARRC was expanded to include quite a number of regulators, banks, GSEs, exchanges, and investment managers. By 2017, the ARRC had settled on SOFR – Secured Overnight Financing Rate – as the replacement for LIBOR and had proposed a transition plan for moving the market from LIBOR to SOFR, the key steps of which are summarized in Figure Intro.1.
Lesser-used USD LIBOR values ceased on 31-Dec-21.
Remaining USD LIBOR values will cease on 30-Jun-23.
Supervisory guidance instructed banks to stop using LIBOR for a reference rate on new products by 31-Dec-21. In fact, continued use of LIBOR as a reference rate for new products was to be considered a “safety and soundness risk.”
For derivatives, LIBOR-SOFR fallback spreads (to be used in legacy products) were set by currency and by tenor on 5-Mar-21.
Legacy Eurodollar futures contracts will be converted to SOFR futures at a fixed spread of 26.161 bp.
For consumer cash products, the LIBOR-SOFR fallback spread for each tenor will be:
Before 1-Jul-23: the median difference between USD LIBOR and SOFR compound in arrears during the previous 10 working days
After 30-Jun-24: the median spread for that tenor during the five years prior to 5-Mar-21
Between 1-Jul-23 and 30-Jun-24: the linearly interpolated value between the two rates above
For institutional cash products, such as corporate loans and floating rate notes, for each tenor the fallback spread is the median of the historical differences between USD LIBOR and the compounded in arrears SOFR value over a five-year period prior to 5 March 2021.
FIGURE Intro.1 Transition from LIBOR to SOFR
Source: Authors
SOFR FUTURES AND OPTIONS: TOPICS AND STRUCTURE OF THIS BOOK
While the International Swaps and Derivatives Association (ISDA) has been overseeing the practical implementation of the LIBOR-to-SOFR transition for over-the-counter derivatives, and while the ARRC has been overseeing the practical implementation of the transition for cash products, the CME has been working to facilitate the transition for listed derivatives, namely futures and options.
The last step of the historical evolution of money markets summarized thus far leads to the subject of our book, SOFR futures and options, and links it with the transition from an unsecured term-rate to a secured overnight rate, implying two fundamental changes:
Term-lending, which used to be based on the term-rate LIBOR, needs to be based on an overnight reference rate.
The transition from LIBOR to SOFR involves the basis between unsecured and secured rates.
The main goal of this book is to provide a conceptual framework for these changes in section 1 and practical help for dealing with them in section 2. Like the subject of this book, SOFR futures and options are historically and conceptually linked to these two fundamental changes. It is the structure of the first part: Chapters 1, 2, and 3 address the implications of switching from a term rate to an overnight rate, and Chapter 4 focuses on the basis.
Chapter 1 outlines the construction of SOFR from the repo market. Since liquidity in the repo market is sufficient only for the shortest tenor, the decision to base lending on a secured reference rate implied the decision to base lending on an overnight rate. This fact is the reason behind the need to migrate the cash loan and derivatives markets from a term rate (LIBOR) to an overnight rate (SOFR).
Chapter 2 describes this migration in the futures markets by comparing SOFR with ED (Eurodollar) contracts. It turns out that it can easily be implemented in the futures market; with the exception of the front month contract, the transition from LIBOR to SOFR as the underlying rate is, for practical purposes, little more than a renaming exercise of ED and FF (Fed Funds) futures. Chapter 2 also provides a fair value model for the spread between 1M and 3M SOFR futures:
The three-month SOFR futures contract settles to a compounded average of SOFR values produced daily by the New York Federal Reserve. This compounded average is quite similar to a geometric average, and it means the SOFR futures
rate
(100 less the SOFR futures price) is equal to the forward rate between the first and last days of the three-month reference period for that contract.
5
In contrast, the one-month SOFR futures contract settles to a
simple
average of SOFR values during the respective calendar month. As a result, the futures rate for a one-month SOFR futures contract is not identical to the forward rate between the first and last days of the relevant reference period. The nature of these differences is highlighted in
Chapters 2
and
6
.
Chapter 3 discusses the implications of this migration in the cash loan markets. Here, unlike for futures, the transition from the forward-looking term rate LIBOR to the backward-looking overnight rate SOFR met significant resistance. Chapter 3 explains how the tension between the goals of regulators and the needs of borrowers has resulted in the compromise of introducing a term rate for SOFR calculated via a model from the SOFR futures market. As a result of using a model, the cost of hedging the term rate with futures is high, and regulators keep it at a high level by prohibiting a secondary market for the SOFR term rate. This chapter finishes by analyzing two possible scenarios for the further evolution of the tension: It could be resolved either by the high hedging costs for the term rate driving cash loan markets to embrace in-arrears conventions, making the term rate superfluous, or by regulators allowing a secondary market for the term rate, which supports its permanence by reducing the hedging costs – maybe after the frictions caused by the prohibition will have become clear.
Chapter 4 then addresses the implications of switching from an unsecured to a secured reference rate. It provides an economic framework and a statistical model to understand the unsecured–secured basis and applies it to analyze the spread between ED and FF futures on one hand and SOFR futures on the other hand. As the model establishes a link between the unsecured–secured basis driving the ED–SOFR futures spread and the CCBS (cross currency basis swap), it allows replacing the CCBS, which is part of many relative value trades, but involves high capital and transaction costs, in some trades with the much cheaper spread future.
Chapter 5 describes the options on SOFR futures and finds that the transition from the term rate LIBOR to an averaged or compounded overnight rate has major implications for the future options:
As soon as the reference period starts, the future option transmogrifies into a path-dependent exotic Asian option. Options on 1M SOFR contracts are then Asian options of the American type with arithmetic averaging, which are a mathematical challenge and for which no pricing formula exists. One consequence of the absence of a way to determine the Greeks – specifically, the delta required for delta hedging – is the relatively late migration of liquidity from ED to SOFR future options; another consequence is an increased difficulty of using SOFR rather than ED future options for hedging caps and floors.
On the other hand, before the reference period starts, options on SOFR futures are standard options referring to a forward rate, which can be priced and analyzed by well-established methods – though the values are quite sensitive to the statistical process chosen. Here, the conclusion from
Chapter 2
, that for most practical purposes the conceptual difference between a term rate and an average or compound of overnight rates can be reduced to a renaming exercise of already known analytic concepts with some extra caution for the front-month contract, can be applied again – precisely by excluding the front month from the consideration.
Chapter 5
summarizes the realized and implied volatility analysis for the secured yield curve, including the distribution of risk and return, which Galen has mentioned in his Foreword. Expanding the secured versus unsecured theme from
Chapter 4
, we also highlight the opportunities for trading options on SOFR futures versus options on ED contracts and hope that the attractiveness of these spread positions will support the transition of liquidity.
Chapter 6
