Foundations of the Pricing of Financial Derivatives E-Book

Robert E. Brooks

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Serie: Frank J. Fabozzi Series
• Sprache: Englisch

Seitenzahl: 970

Veröffentlichungsjahr: 2024

Beschreibung

An accessible and mathematically rigorous resource for masters and PhD students In Foundations of the Pricing of Financial Derivatives: Theory and Analysis two expert finance academics with professional experience deliver a practical new text for doctoral and masters' students and also new practitioners. The book draws on the authors extensive combined experience teaching, researching, and consulting on this topic and strikes an effective balance between fine-grained quantitative detail and high-level theoretical explanations. The authors fill the gap left by books directed at masters'-level students that often lack mathematical rigor. Further, books aimed at mathematically trained graduate students often lack quantitative explanations and critical foundational materials. Thus, this book provides the technical background required to understand the more advanced mathematics used in this discipline, in class, in research, and in practice. Readers will also find: * Tables, figures, line drawings, practice problems (with a solutions manual), references, and a glossary of commonly used specialist terms * Review of material in calculus, probability theory, and asset pricing * Coverage of both arithmetic and geometric Brownian motion * Extensive treatment of the mathematical and economic foundations of the binomial and Black-Scholes-Merton models that explains their use and derivation, deepening readers' understanding of these essential models * Deep discussion of essential concepts, like arbitrage, that broaden students' understanding of the basis for derivative pricing * Coverage of pricing of forwards, futures, and swaps, including arbitrage-free term structures and interest rate derivatives An effective and hands-on text for masters'-level and PhD students and beginning practitioners with an interest in financial derivatives pricing, Foundations of the Pricing of Financial Derivatives is an intuitive and accessible resource that properly balances math, theory, and practical applications to help students develop a healthy command of a difficult subject.

Leseprobe

The Frank J. Fabozzi Series

Fixed Income Securities, Second Edition

by Frank J. Fabozzi

Focus on Value: A Corporate and Investor Guide to Wealth Creation

by James L. Grant and James A. Abate

Handbook of Global Fixed Income Calculations

by Dragomir Krgin

Managing a Corporate Bond Portfolio

by Leland E. Crabbe and Frank J. Fabozzi

Real Options and Option‐Embedded Securities

by William T. Moore

Capital Budgeting: Theory and Practice

by Pamela P. Peterson and Frank J. Fabozzi

The Exchange‐Traded Funds Manual

by Gary L. Gastineau

Professional Perspectives on Fixed Income Portfolio Management, Volume 3

edited by Frank J. Fabozzi

Investing in Emerging Fixed Income Markets

edited by Frank J. Fabozzi and Efstathia Pilarinu

Handbook of Alternative Assets

by Mark J. P. Anson

The Global Money Markets

by Frank J. Fabozzi, Steven V. Mann, and Moorad Choudhry

The Handbook of Financial Instruments

edited by Frank J. Fabozzi

Collateralized Debt Obligations: Structures and Analysis

by Laurie S. Goodman and Frank J. Fabozzi

Interest Rate, Term Structure, and Valuation Modeling

edited by Frank J. Fabozzi

Investment Performance Measurement

by Bruce J. Feibel

The Handbook of Equity Style Management

edited by T. Daniel Coggin and Frank J. Fabozzi

Foundations of Economic Value Added, Second Edition

by James L. Grant

Financial Management and Analysis, Second Edition

by Frank J. Fabozzi and Pamela P. Peterson

Measuring and Controlling Interest Rate and Credit Risk, Second Edition

by Frank J. Fabozzi, Steven V. Mann, and Moorad Choudhry

Professional Perspectives on Fixed Income Portfolio Management, Volume 4

edited by Frank J. Fabozzi

The Handbook of European Fixed Income Securities

edited by Frank J. Fabozzi and Moorad Choudhry

The Handbook of European Structured Financial Products

edited by Frank J. Fabozzi and Moorad Choudhry

The Mathematics of Financial Modeling and Investment Management

by Sergio M. Focardi and Frank J. Fabozzi

Short Selling: Strategies, Risks, and Rewards

edited by Frank J. Fabozzi

The Real Estate Investment Handbook

by G. Timothy Haight and Daniel Singer

Market Neutral Strategies

edited by Bruce I. Jacobs and Kenneth N. Levy

Securities Finance: Securities Lending and Repurchase Agreements

edited by Frank J. Fabozzi and Steven V. Mann

Fat‐Tailed and Skewed Asset Return Distributions

by Svetlozar T. Rachev, Christian Menn, and Frank J. Fabozzi

Financial Modeling of the Equity Market: From CAPM to Cointegration

by Frank J. Fabozzi, Sergio M. Focardi, and Petter N. Kolm

Advanced Bond Portfolio Management: Best Practices in Modeling and Strategies

edited by Frank J. Fabozzi, LionelMartellini, and Philippe Priaulet

Analysis of Financial Statements, Second Edition

by Pamela P. Peterson and Frank J. Fabozzi

Collateralized Debt Obligations: Structures and Analysis, Second Edition

by Douglas J. Lucas, Laurie S. Goodman, and Frank J. Fabozzi

Handbook of Alternative Assets, Second Edition

by Mark J. P. Anson

Introduction to Structured Finance

by Frank J. Fabozzi, Henry A. Davis, and Moorad Choudhry

Financial Econometrics

by Svetlozar T. Rachev, Stefan Mittnik, Frank J. Fabozzi, Sergio M. Focardi, and Teo Jasic

Developments in Collateralized Debt Obligations: New Products and Insights

by Douglas J. Lucas, Laurie S. Goodman, Frank J. Fabozzi, and Rebecca J. Manning

Robust Portfolio Optimization and Management

by Frank J. Fabozzi, Petter N. Kolm, Dessislava A. Pachamanova, and Sergio M. Focardi

Advanced Stochastic Models, Risk Assessment, and Portfolio Optimizations

by Svetlozar T. Rachev, Stogan V. Stoyanov, and Frank J. Fabozzi

How to Select Investment Managers and Evaluate Performance

by G. Timothy Haight, Stephen O. Morrell, and Glenn E. Ross

Bayesian Methods in Finance

by Svetlozar T. Rachev, John S. J. Hsu, Biliana S. Bagasheva, and Frank J. Fabozzi

Structured Products and Related Credit Derivatives

by Brian P. Lancaster, Glenn M. Schultz, and Frank J. Fabozzi

Quantitative Equity Investing: Techniques and Strategies

by Frank J. Fabozzi, Sergio M. Focardi, and Petter N. Kolm

Introduction to Fixed Income Analytics, Second Edition

by Frank J. Fabozzi and Steven V. Mann

The Handbook of Traditional and Alternative Investment Vehicles

by Mark J. P. Anson, Frank J. Fabozzi, and Frank J. Jones

The Theory and Practice of Investment Management, Second Edition

edited by Frank J. Fabozzi and Harry M. Markowitz

Foundations of the Pricing of Financial Derivatives

Theory and Analysis

ROBERT E. BROOKSDON M. CHANCE

Copyright © 2024 by Robert E. Brooks and Don M. Chance. All rights reserved.

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

Published simultaneously in Canada.

No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per‐copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750‐8400, fax (978) 750‐4470, or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748‐6011, fax (201) 748‐6008, or online at http://www.wiley.com/go/permission.

Trademarks: Wiley and the Wiley logo are trademarks or registered trademarks of John Wiley & Sons, Inc. and/or its affiliates in the United States and other countries and may not be used without written permission. All other trademarks are the property of their respective owners. John Wiley & Sons, Inc. is not associated with any product or vendor mentioned in this book.

Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Further, readers should be aware that websites listed in this work may have changed or disappeared between when this work was written and when it is read. Neither the publisher nor authors shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages.

For general information on our other products and services or for technical support, please contact our Customer Care Department within the United States at (800) 762‐2974, outside the United States at (317) 572‐3993 or fax (317) 572‐4002.

Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic formats. For more information about Wiley products, visit our web site at www.wiley.com.

Library of Congress Cataloging‐in‐Publication Data:

Names: Brooks, Robert E., 1960- author. | Chance, Don M., author.

Title: Foundations of the pricing of financial derivatives : theory and analysis / Robert E. Brooks & Don M. Chance.

Description: Hoboken, New Jersey : Wiley, [2024] | Series: Frank J. Fabozzi series | Includes bibliographical references and index.

Identifiers: LCCN 2023044922 (print) | LCCN 2023044923 (ebook) | ISBN 9781394179657 (cloth) | ISBN 9781394179671 (adobe pdf) | ISBN 9781394179664 (epub)

Subjects: LCSH: Derivative securities—Prices.

Classification: LCC HG6024.A3 B765 2024 (print) | LCC HG6024.A3 (ebook) | DDC 332.64/57—dc23/eng/20231027

LC record available at https://lccn.loc.gov/2023044922

LC ebook record available at https://lccn.loc.gov/2023044923

Cover Design: Wiley

Cover Image: © Jeremy Horner/Getty Images

Preface

Teaching graduate students in finance must be the second best job in the world, next to parenting. Finance is such a rich and exciting subject, and it is uncommon to teach a student who is not interested. Now, we did not say they all put in the maximum effort, but they seldom act as if they are bored. After all, everyone wants to know more about money. Finance professors are the envy of their relatives, and they typically command a great deal of attention at family reunions and receptions with everyone hoping to learn just one iota of information that might make them financially better off.

The authors of this book have taught graduate students in finance for many decades (we stopped counting while we were still young!), and we can attest that our students have taught us a great deal, too. But as longtime teachers of advanced masters and doctoral students, we have been concerned that it is possible to get one of these impressive advanced degrees and circumvent, or just never have, the opportunity to get familiar with the principles of financial derivative pricing. Corporate finance and asset pricing are the core of what we do in the academic finance field. But if a corporate finance or asset pricing specialist is not exposed to derivative pricing, they are missing out on a rich body of knowledge that can help them do their jobs. Or at least half‐way understand when a derivatives person presents a paper.

This book had its origin in a set of teaching notes that one of the authors (Chance) began writing in 1996. These notes were designed to fill what he saw as a void in instructional material at the advanced level. Well, it was either that or he just wanted it done his way. These notes were posted on the Web and eventually grew in number to almost 60. The notes were short, often less than 10 pages, tightly contained treatments of various topics. He received a great deal of recognition from complete strangers around the world, and in time, the notes were morphed into this book. He thought it would be easy just to turn the notes into a book. But that led to two problems.

The first was that we had to remove the notes from the Web, leading to some disappointment from fans. Although we had given away much of this material, publishers expect that you will protect their investment by not giving it away any longer. The second problem was that a multiplicity of notation was used in the notes. They were never written as a unified whole. As such, we had a great deal of cleaning up to do. And, we suppose, a third problem was that the notes did not cover the entire field, so yes, we had a lot more writing to do.

This book in manuscript form has been class‐tested three times. This course was a doctoral seminar that was open to finance masters and doctoral students and also STEM students across the university. All of these students contributed a great deal to catching errors, forcing us to rethink how we said something, and in some cases contributing end‐of‐chapter problems. This book would be nowhere near ready for prime time were it not for them. Because these students endured rough drafts of this book, I would like to thank them by name: Brecklyn Groce, Dennel McKenzie, Jeremy Vasseur, Paul Mahoney, Tengfei Zhang, Nha Tran, Nur Faisal, Jason Priddle, Mehdi Khorram, Mengmeng Liu, Phuc An Vinh Nguyen, Santoshi Rimal, Cameron Roman, Gillian Sims, Pujan Shrestha, Yuanyi Zhang, Aihuan Zhang, Fouad Hasan, Junior Betanco, Ravi Joshi, and Yingying Guo. We also thank Chance's research assistant, Stephanie Hoskins, for additional comments.

A special note of thanks is extended to Chance's PhD student, Amber Schreve, who carefully read and edited the entire book, catching a number of errors and typos, questioning sentences that might not have made complete sense to the reader, and offering many suggestions for improvements. Amber's background in teaching math to undergraduates challenged us to strive for the highest level of clarity that we could.

We never set out to write this book. As noted, it sprung from Chance's teaching notes. And we also agreed not to attempt to compete with highly technical books on quantitative finance and financial engineering written by STEM scholars. What we wanted to do was create a book that was within reach of PhD and advanced masters' students in finance, many of whom do not have the technical backgrounds of STEM students. So, do not expect to find everything on the subject here. But you will find a broad, relatively technical overview of the most important knowledge you need to know to build a solid foundation for understanding the pricing of financial derivatives.

Like all authors, we think we accomplished that. We know, in all honesty, that there are inevitably failures that even another 10 years of editing and class‐testing would not completely eliminate. We accept full responsibility for any such deficiencies and promise to consider them if the book goes into a future edition. If you want to communicate with us on any such matters, please send an email to [email protected] and [email protected].

The least likely people in the world to email us with a problem in the book are our families. And they deserve credit for just being there and not complaining that we were writing another book when it seemed like we just finished the last one. Don would like to thank his wife, Jan, and their adult and married daughters, Kim and Ashley, and their families. Robert would like to thank his wife, Ann, and their adult and married six children and similarly their constantly increasing number of grandchildren.

Robert E. BrooksTuscaloosa, AL

Don M. ChanceBaton Rouge, LA

CHAPTER 1Introduction and Overview

Finance is the study of money, something commonly used as a medium of exchange. It involves the measurement and management of money: how much we had, how much we have, and how much we expect to have in the future. Much of what we study and do in finance, however, is about making money, so its focus tends to be on the future. Yet, the future is unknown, and the unknown is about risk. People take risks in order to earn money. Finance is essentially the study of the risk and return of money.

In order to do what we do in finance, we must measure money. In fact, measurement in terms of monetary units, such as US dollars, is a core activity of finance, and there is considerably more to measuring money than just counting it. The challenge in finance is in measuring the value of assets that are not cash but can be expressed in terms of cash. An instrument is a generic term that refers to a tool that measures something. A financial instrument is a type of instrument defined as a tool that measures something in dollars or other currency units. In our context, positive‐valued financial instruments are called assets and negative‐valued financial instruments are called liabilities. In general, assets and liabilities are both categorized as instruments or financial instruments because our focus is on finance. Thus, an instrument can reference either assets or liabilities.

Some instruments trade in a market where we can observe their prices, but does that mean that we do not question whether these prices are good prices, in the sense of fairly and accurately reflecting what something should be worth? If you need to buy a used car and you find a 10‐year‐old car with 150,000 miles on it selling for $50,000, does that mean you would pay that price? No, it is likely you would believe that price to be too high. Perhaps $5,000 is a better price. What we have just done is a valuation of the car. We may have gotten it from some service, observed the prices of similar cars, or simply said that $5,000 is the amount we would pay, meaning that we would willingly part with the consumption of $5,000 of other goods and services to obtain the car.

Likewise, securities that trade in markets have prices that are observable, but that does not mean that we accept those prices as fair. These securities need to be valued, meaning to assign a number to them that represents what one thinks is a fair price. If the value assigned by the investor exceeds the price at which the security is trading in the market, the security is attractively priced and would suggest that the investor should buy the security. If the value assigned by the investor is below the price at which the security is trading in the market, the security is unattractively priced and would suggest that the investor should sell the security if they own it, short sell it if they do not own it, or simply not trade it at all.

We now explain our motivation for writing Foundations of the Pricing of Financial Derivatives.

1.1 MOTIVATION FOR THIS BOOK

Many finance courses focus on valuing stocks and bonds. Yet, there is also another family of financial instruments known as derivatives, and valuing derivatives is one of the most technical subjects in finance. It requires not only setting up a model of the prices of assets that trade in the market but also establishing a means by which one can connect the derivative to the asset on which the derivative is based. There is a great deal of technical knowledge that must transfer from instructor to student. Much of that knowledge can seem cryptic and inaccessible, though that could be a bit of an overreaction from the fear of learning something new. However, those who know this subject reasonably well can easily fall into the trap of assuming that those who do not know this subject well should find the subject easy. That is the pitfall of being a scholar. A scholar thinks that material in which they have expertise in is not that difficult, when in fact, it really is quite challenging. What a scholar should do in conveying knowledge, however, is to recall how it was when they were learning it. In other words, putting oneself in the student's shoes and empathizing with the student will result in the most successful learning environment. That is indeed one of the overriding objectives of this book: to teach some seemingly complex material in a very user‐friendly way.

For without a doubt, teaching and learning advanced material in finance is challenging to the instructor and to the student. Indeed, one of the greatest challenges for instructors in advanced graduate courses in finance is to cover a large body of highly technical information in a relatively short course of study. Well‐prepared students make it a lot easier, but student preparation is often not at the desired level, and classes are frequently filled with students with varying degrees of preparation. In an ideal world, such students would have previously had courses in probability, calculus, linear algebra, coding, stochastic processes, econometrics, numerical analysis, non‐parametric statistics, differential equations, microeconomics and macroeconomics, and last but certainly not least, finance. It is common for faculty members and students alike to complain that students are inadequately prepared for the technical rigors of advanced graduate study in finance. This book is an effort to address this problem by leveling the base of preparation.

The degree of preparation of finance students is typically a function of the program in which the student is enrolled. Graduate study in finance can generally be done in one of three types of programs. One is an MBA, which usually comprises two years of study, the first consisting of a core set of business courses, of which a broad survey of finance is typically one component. The second year of an MBA is composed of a few required courses in general business but largely permits students to tailor their programs toward their specialized interests. Many students choose to take second‐year courses in finance. The MBA is usually the marquee program at top‐tier universities, a large money‐maker, and is designed to draw students with degrees from all undergraduate disciplines. Hence, the first‐year finance course starts at the very foundations of the subject with such topics as time value of money and discounted cash flow valuation, ultimately moving on to understanding financial markets, the relationship between risk and return, market efficiency, and corporate capital structure and dividend policy. Though some MBA students have technical backgrounds, most do not. Hence, MBA students will often struggle with advanced finance courses that are particularly quantitative.

A second form of masters' level study in finance is the specialized master's degree in finance, often called an MS or master of science, and sometimes MSF for master of science in finance. Such a program provides concentrated graduate study in finance, typically over a period of one to two academic years. There may be certain core or required courses, and students are usually allowed to take electives in their preferred areas of finance. Students in this type of program will almost always have previously studied finance and will tend to have more technical backgrounds than the average MBA student.

The third type of program in finance is the doctor of philosophy or PhD. This degree, requiring a minimum of four years, is an intensive research‐oriented program that requires all students to achieve a high level of understanding of theoretical models and empirical research methods.1 It is here that the greatest problem lies in giving students a sufficient level of technical knowledge without sacrificing the time they need to devote to seminars in the various areas of finance. When students are accepted into PhD programs in finance, they are typically required to have a solid foundation in math. But, the definition of a “solid foundation in math” can vary, and merely taking some math courses and making good grades is not necessarily enough. Most finance PhD students, even those with strong math backgrounds, learn something new about math while in their PhD programs. Students who have been accepted into PhD programs are often advised to take more math courses before starting the program. They usually do, but it does not often help nearly as much as one might think.

Let us be clear. Finance is not mathematics. Mathematics is a set of tools used in finance. But just as one cannot build furniture efficiently without knowledge of how to use tools, one cannot understand finance without having the necessary tools of mathematics.

And, as noted, one of the most technical subjects in finance is derivative pricing theory. Sometimes it can be even difficult to keep terms straight because terms can mean different things in different settings. Throughout this book, we will use price and value interchangeably as is financial industry custom. Technically, the concept of price refers to the monetary amount that is exchanged when something is traded, irrespective of what one thinks the item is worth. Value refers to an instrument's non‐observed monetary amount as assigned by a market participant. The individual may or may not be using a formal mathematical model. Thus, technically, formal models in finance, such as the capital asset pricing model (CAPM) and the Black‐Scholes‐Merton option pricing model (BSMOPM), should have been termed the capital asset valuation model (CAVM) and the Black‐Scholes‐Merton option valuation model (BSMOVM). Theoretical models are just a means of expressing one's view on value. As we will see later, arbitrage activity typically moves observed market prices to the arbitrageur's value. Hence, we will stick with financial industry custom even though value will always have higher levels of epistemic uncertainty when compared to the market price.

Although the majority of finance faculty and PhD students will not specialize in derivatives, there is no doubt that a solid understanding of derivative pricing theory is an important element of doctoral‐level education in finance. Derivative pricing theory, in particular the Black‐Scholes‐Merton model, has had a tremendous impact on finance. It has provided a framework for understanding not only standard derivatives, such as options, but also it has shown us that derivatives can explain many other topics and relationships in finance, such as callable bonds, convertible bonds, credit risk, and corporate capital structure. The impact of derivative pricing theory has been so great that Nobel Prizes were awarded in 1995 to Myron Scholes and Robert Merton with special recognition to the late Fischer Black for work on this subject. Yet, with the increasing need for students to take so many courses in econometrics and statistics, there is often little room in a doctoral program for such a course.

Our goal is to introduce the vast financial derivatives markets to PhD students and others in hopes that it will stimulate your interest in research related to financial derivatives, as well as aid in your future research agenda, even if your agenda is not explicitly financial derivatives. By way of introduction, we present selected derivatives market prices in Table 1.1.2 Derivatives market prices are unique and often convey cloaked information. On completion of this book, you will be better able to rightfully interpret what information is and is not conveyed.

Table 1.1 Panel A shows natural gas futures prices. Notice that the key descriptor is the delivery month. We denote the current year as Y1. Thus, the December Y1 last traded futures price is $2.896/MMBtu (million British thermal units). Note that futures prices generally rise for longer maturities with the exception of September.3 The aggregate open interest is the number of either long or short positions currently outstanding. Each contract is for 10,000 MMBtu. Thus, the natural gas futures market currently represents 12,689,550,000 MMBtus.

Table 1.1 Panel B shows option prices of the SPY, which is the exchange‐traded fund of the S&P 500 Index. With options, the key descriptors are more complex requiring both the maturity date expressed in days to maturity here and strike price. For example, the 114‐day call price with strike price $280/share is $10.40/share and the corresponding put price is $9.76/share. Notice that with longer maturities, similar strike options have higher prices. Further, call prices decline for higher strike prices, whereas put prices rise for higher strike prices. You will learn why later in this book.

Table 1.1 Panel C shows interest rate swap rates. For example, a five‐year swap was quoted at 2.022%. The mid fixed rate is the average of the bid and ask rate for the fixed leg of a fixed‐for‐floating interest rate swap. Notice that this fixed rate initially declines and then subsequently rises for longer maturities.4

Table 1.1 Panel D shows 1‐month secured overnight financing rate (SOFR) futures data.5 The data provided here are rate‐based and hence show the implied interest rates rather than quoted prices. The interest rate is simply 100 minus the quoted price. For example, the November Y1 rate of 5.400 implies a quoted price of 94.600. Each SOFR futures contract is for $5,000,000 notional amount on 1‐month interest rates. At this point, just notice the aggregate open interest is 704,883. Open interest is the number of long contracts outstanding. Thus, the total number of contracts outstanding, representing both long and short positions as this is an exchange‐traded contract, is 1,409766 [= 2(704,883)]. As each contract is for $5,000,000 notional, the aggregate notional amount represented by this one market is $7,048,830,000,000 or over $7 trillion. The notional amount or simply notional is the implied principal on which interest calculations are based. Thus, without explaining all this data in great detail, clearly the derivatives industry is large and involves numerous interesting complexities worthy of investigation.

TABLE 1.1 Panel A. Selected Derivatives Markets Prices: Selected Natural Gas Futures Prices

Description

Price

Change

Open Interest

Volume

JunY1

2.615

+.033

  9,781

 2,311

JulY1

2.620

+.036

353,254

22,906

AugY1

2.627

+.034

 92,888

 4,108

SepY1

2.618

+.031

177,123

 2,905

OctY1

2.651

+.030

122,641

 2,001

NovY1

2.727

+.027

 81,686

 1,057

DecY1

2.896

+.026

 99,738

   878

. . .

. . .

. . .

. . .

. . .

Note: Aggregate Open Interest = 1,268,955; Volume = 38,910.

TABLE 1.1 Panel B. Selected Option Prices on S&P 500 Index Exchange‐Traded Fund (SPY)

Maturity (Days)

Strike Price

Call Price

Put Price

 30

279

 5.97

 4.94

 30

280

 5.43

 5.39

 30

281

 4.85

 5.82

 51

279

 7.39

 6.22

 51

280

 6.80

 6.63

 51

281

 6.18

 7.06

 79

279

 9.33

 7.59

 79

280

 8.67

 8.02

 79

281

 7.93

 8.39

114

279

11.04

 9.30

114

280

10.40

 9.76

114

281

 9.96

10.04

. . .

. . .

. . .

. . .

Note: Spot SPY = 280.15.

TABLE 1.1 Panel C. Interest Rate Swaps

Tenor

Mid Fixed Rate

1 Year

2.350

2 Year

2.115

3 Year

2.032

5 Year

2.022

10 Year

2.175

20 Year

2.352

30 Year

2.378

TABLE 1.1 Panel D. Secured Overnight Financing Rate Futures Contracts

Description

Implied Rate

Change

Open Interest

Volume

AugY1

5.305

UNCH

275,240

 1,362

SepY1

5.325

+0.005

105,264

 2,839

OctY1

5.455

+0.005

 94,418

22,034

NovY1

5.400

+0.005

106,863

13,293

DecY1

5.395

UNCH

 47,427

 4,810

JanY2

5.480

–0.005

 32,062

 7,439

FebY2

5.300

–0.005

 19,308

 5,216

. . .

. . .

. . .

. . .

. . .

Note: Aggregate Open Interest = 704,883; Volume = 75,845.