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- Herausgeber: John Wiley & Sons
- Kategorie: Fachliteratur
- Serie: Wiley Finance Editions
- Sprache: Englisch
Explore the foundations of modern finance with this intuitive mathematical guide In Mathematical Techniques in Finance: An Introduction, distinguished finance professional Amir Sadr delivers an essential and practical guide to the mathematical foundations of various areas of finance, including corporate finance, investments, risk management, and more. Readers will discover a wealth of accessible information that reveals the underpinnings of business and finance. You'll learn about: * Investment theory, including utility theory, mean-variance theory and asset allocation, and the Capital Asset Pricing Model * Derivatives, including forwards, options, the random walk, and Brownian Motion * Interest rate curves, including yield curves, interest rate swap curves, and interest rate derivatives Complete with math reviews, useful Excel functions, and a glossary of financial terms, Mathematical Techniques in Finance: An Introduction is required reading for students and professionals in finance.
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Veröffentlichungsjahr: 2022
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Table of Contents
Cover
Title Page
Copyright
Dedication
Preface
BACKGROUND
BOOK STRUCTURE
Acknowledgments
About the Author
Acronyms
CHAPTER 1: Finance
1.1 FOLLOW THE MONEY
1.2 FINANCIAL MARKETS AND PARTICIPANTS
1.3 QUANTITATIVE FINANCE
CHAPTER 2: Rates, Yields, Bond Math
2.1 INTEREST RATES
2.2 ARBITRAGE, LAW OF ONE PRICE
2.3 PRICE‐YIELD FORMULA
2.4 SOLVING FOR YIELD: ROOT SEARCH
2.5 PRICE RISK
2.6 LEVEL PAY LOAN
2.7 YIELD CURVE
EXERCISES
PYTHON PROJECTS
CHAPTER 3: Investment Theory
3.1 UTILITY THEORY
3.2 PORTFOLIO SELECTION
3.3 CAPITAL ASSET PRICING MODEL
3.4 FACTORS
3.5 MEAN‐VARIANCE EFFICIENCY AND UTILITY
3.6 INVESTMENTS IN PRACTICE
REFERENCES
EXERCISES
PYTHON PROJECTS
CHAPTER 4: Forwards and Futures
4.1 FORWARDS
4.2 FUTURES CONTRACTS
4.3 STOCK DIVIDENDS
4.4 FORWARD FOREIGN CURRENCY EXCHANGE RATE
4.5 FORWARD INTEREST RATES
REFERENCES
EXERCISES
CHAPTER 5: Risk‐Neutral Valuation
5.1 CONTINGENT CLAIMS
5.2 BINOMIAL MODEL
5.3 FROM ONE TIME‐STEP TO TWO
5.4 RELATIVE PRICES
REFERENCES
EXERCISES
CHAPTER 6: Option Pricing
6.1 RANDOM WALK AND BROWNIAN MOTION
6.2 BLACK‐SCHOLES‐MERTON CALL FORMULA
6.3 IMPLIED VOLATILITY
6.4 GREEKS
6.5 DIFFUSIONS, ITO
6.6 CRR BINOMIAL MODEL
6.7 AMERICAN‐STYLE OPTIONS
6.8 PATH‐DEPENDENT OPTIONS
6.9 EUROPEAN OPTIONS IN PRACTICE
REFERENCES
EXERCISES
PYTHON PROJECTS
CHAPTER 7: Interest Rate Derivatives
7.1 TERM STRUCTURE OF INTEREST RATES
7.2 INTEREST RATE SWAPS
7.3 INTEREST RATE DERIVATIVES
7.4 INTEREST RATE MODELS
7.5 BERMUDAN SWAPTIONS
7.6 TERM STRUCTURE MODELS
7.7 INTEREST RATE DERIVATIVES IN PRACTICE
REFERENCES
EXERCISES
APPENDIX A: Math and Probability Review
A.1 CALCULUS AND DIFFERENTIATION RULES
A.2 PROBABILITY REVIEW
A.3 LINEAR REGRESSION ANALYSIS
APPENDIX B: Useful Excel Functions
About the Companion Website
Index
End User License Agreement
List of Tables
Chapter 1
TABLE 1.1 Balance sheet of the United States at 2020 year end.
TABLE 1.2 Households sector balance sheet as of 2020 year end.
TABLE 1.3 Market size ($Trillions).
TABLE 1.4 U.S. bond market ($Trillions).
TABLE 1.5 Global derivatives market size ($Trillions).
TABLE 1.6 Market participants and financial products.
Chapter 2
TABLE 2.1 Future Value of $100,000 for a 2 year (
) loan with
per annum.
TABLE 2.2 Interest for principal of $1,000,000 and interest rate
per year ...
TABLE 2.3 Sensitivity measures for three different bonds.
TABLE 2.4 Discount factor curve construction via bootstrap method.
TABLE 2.5 Hint for bootstrap problem.
Chapter 3
TABLE 3.1 St. Petersburg game.
TABLE 3.2 MVP portfolio for two risky assets.
TABLE 3.3 Regression statistics.
Chapter 4
TABLE 4.1 3‐month evolution of an asset and its forward price.
Chapter 6
TABLE 6.1 Properties of normal and lognormal random variables.
TABLE 6.2 Six‐month call option prices with different strikes.
TABLE 6.3 Six‐month put option prices with different strikes.
TABLE 6.4 BSM formulas and Greeks.
TABLE 6.5 10 x 1000‐path simulation runs, random.seed(2021).
Chapter 7
TABLE 7.1 Fixed leg's cash flows of a $100M 1‐year 4% fixed versus floating ...
TABLE 7.2 Floating leg's cash flows of a $100M 1‐year 4% fixed versus floati...
TABLE 7.3 Discount factor curve, forward 6‐month rate curve, and swap rates ...
TABLE 7.4 1‐year forward start 1‐year quarterly cap with strike
.
TABLE 7.5 Discount factor curve at each node.
TABLE 7.6 Value of $1M 6 month into a 1.5‐year Bermudan 4% p.a. semiannual s...
List of Illustrations
Chapter 2
FIGURE 2.1 Bond price versus yield with coupon rate = 2% p.a.
FIGURE 2.2 Price of bond versus remaining years to maturity.
FIGURE 2.3 Pull to par effect for a 2‐year, 4% semiannual coupon bond.
FIGURE 2.4 Cash flows of a 2‐year 4% semiannual coupon bond versus a 2‐year ...
FIGURE 2.5 Newton‐Raphson method.
FIGURE 2.6 PV01, PVBP, and modified duration of a coupon bond.
FIGURE 2.7 Interest and principal payments of a level pay loan.
FIGURE 2.8 A pool of loans with low prepayment speed.
FIGURE 2.9 A pool of loans with high prepayment speed.
FIGURE 2.10 Negative convexity due to increased prepayments when rates are l...
FIGURE 2.11 U.S. Treasury yield curve.
Chapter 3
FIGURE 3.1 Compound lottery.
FIGURE 3.2 Risk attitude and utility function.
FIGURE 3.3 Risk premium for a risk‐averse investor.
FIGURE 3.4 Conic sections.
FIGURE 3.5 Feasible region for two risky assets.
FIGURE 3.6 Feasible regions for different correlations.
FIGURE 3.7 Feasible region for three or more risky assets.
FIGURE 3.8 Method of Lagrange multipliers.
FIGURE 3.9 Relationship between CML and the feasible region of risky assets....
FIGURE 3.10 Proof of the CAPM formula.
FIGURE 3.11 PCA identification of eigenvectors.
FIGURE 3.12 Utility indifference curves.
FIGURE 3.13 5‐year monthly price history of Amazon (AMZN), Walmart (WMT).
FIGURE 3.14 Walmart (WMT) versus Amazon (AMZN).
FIGURE 3.15 Z‐Score for Amazon‐Walmart pair trade.
FIGURE 3.16 10,000 risky portfolios.
Chapter 4
FIGURE 4.1 Contango versus backwardation.
FIGURE 4.2 3‐month evolution of an asset's spot and forward prices.
Chapter 5
FIGURE 5.1 Economic value of European‐style call and put options at expirati...
FIGURE 5.2 One‐step binomial model.
FIGURE 5.3 Lack of arbitrage.
FIGURE 5.4 Two‐step binomial model.
FIGURE 5.5 Two‐period evolution of the replicating portfolio for a call opti...
FIGURE 5.6 A symmetric random walk is a martingale.
Chapter 6
FIGURE 6.1 Standard Brownian motion.
FIGURE 6.2 Geometric Brownian motion.
FIGURE 6.3 Random walk with drift (top); exponentiated random walk with drif...
FIGURE 6.4 Normal and lognormal random variables with same mean and variance...
FIGURE 6.5 European‐style option payoffs.
FIGURE 6.6 Skew and smile effect for out‐of‐the‐money options.
FIGURE 6.7 Call option value and its delta.
FIGURE 6.8 Put option value and its delta.
FIGURE 6.9 Convexity PnL versus time decay for a delta‐hedged call option.
FIGURE 6.10 Delta as a function of time to expiration,
.
FIGURE 6.11 CRR binomial model.
FIGURE 6.12 Backward induction algorithm.
FIGURE 6.13 Two antithetic sample paths in a random walk.
FIGURE 6.14 Convergence of CRR model to BSM Formula.
FIGURE 6.15 Convergence of backward induction model to the American option....
Chapter 7
FIGURE 7.1 Forward‐rate, zero‐coupon, and discount‐factor curves.
FIGURE 7.2 Cash flows of a 1‐year USD fixed versus floating interest rate sw...
FIGURE 7.3 Payoff of a
into
‐year payer swaption.
FIGURE 7.4 Typical implementation of the Hull‐White model.
FIGURE 7.5 Navigating the sublattice originating from each node to extract t...
FIGURE 7.6 Forward induction and pure security prices.
FIGURE 7.7 Two‐year evolution of the 6‐month rate.
FIGURE 7.8 Full term structure model.
Appendix A
FIGURE A.1 Probability density function of a normal
random variable.
Guide
About the Companion Website
Cover Page
Title Page
Copyright
Dedication
Preface
Acknowledgments
About the Author
Acronyms
Table of Contents
Begin Reading
Appendix A Math and Probability Review
Appendix B Useful Excel Functions
Index
End User License Agreement
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Mathematical Techniques in Finance
An Introduction
AMIR SADR
Copyright © 2022 by John Wiley & Sons, Inc. All rights reserved.
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Library of Congress Cataloging-in-Publication Data:
Names: Sadr, Amir, author.
Title: Mathematical techniques in finance : an introduction / Amir Sadr.
Description: Hoboken, New Jersey : John Wiley & Sons, Inc., [2022] | Series: Wiley finance series | Includes index.
Identifiers: LCCN 2022000565 (print) | LCCN 2022000566 (ebook) | ISBN 9781119838401 (cloth) | ISBN 9781119838425 (adobe pdf) | ISBN 9781119838418 (epub)
Subjects: LCSH: Finance–Mathematical models.
Classification: LCC HG106 .S23 2022 (print) | LCC HG106 (ebook) | DDC 332.01/5195–dc23/eng/20220112
LC record available at https://lccn.loc.gov/2022000565
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To my students
Preface
Finance as a distinct field from economics is generally defined as the science or study of the management of funds. The creation of credit, savings, investments, banking institutions, financial markets and products, and risk management all fall under the purview of finance. The unifying themes in finance are time, risk, and money.
Mathematical or quantitative finance is the application of mathematics to these core areas. While simple arithmetic was enough for accounting and keeping ledgers and double‐entry bookkeeping, Louis Bachelier's doctoral thesis, Théorie de la spéculation and published in 1900, used Brownian motion to study stock prices, and is widely recognized as the beginning of quantitative finance. Since then, the use of increasingly sophisticated and specialized mathematics has created the modern field of quantitative finance encompassing investment theory, asset pricing, derivatives, financial data science, and the emerging area of crypto assets and Decentralized Finance (DeFi).
BACKGROUND
This book is the collection of my lecture notes for an elective senior level undergraduate course on mathematics of finance at NYU Courant. The mostly senior and some first year graduate students come from different majors with an even distribution of mathematics, engineering, economics, and business majors. The prerequisites for the book are the same as the ones for the course: basic calculus, probability, and linear algebra. The goal of the book is to introduce the mathematical techniques used in different areas of finance and highlight their usage by drawing from actual markets and products.
BOOK STRUCTURE
A simple definition of finance would be the study of money; quantitative finance could be thought of as the mathematics of money. While reductive and simplistic, this book uses this metaphor and follows the money across different markets to motivate and introduce concepts and mathematical techniques.
Bonds
In Chapter 2, we start with the basic building blocks of interest rates and time value of money to price and discount future cash flows for fixed income and bond markets. The concept of compound interest and its limit as continuous compounding is the first foray into mathematics of finance. Coupon bonds make regular interest payments, and we introduce the Geometric series to derive the classic bond price‐yield formula.
As there is generally no closed form formula for implied calculations such as implied yield or volatility given a bond or option price, these calculations require numerical root‐solving methods and we present the Newton‐Raphson method and the more robust and popular bisection method.
The concept of risk is introduced by considering the bond price sensitivity to interest rates. The Taylor series expansion of a function provides the first and second order sensitivities leading to duration and convexity for bonds in Chapter 2, and delta and gamma for options in Chapter 6. Similar first and second order measures are the basis of the mean‐variance theory of portfolio selection in Chapter 3.
In the United States, households hold the largest amount of net worth, followed by firms, while the U.S. government runs a negative balance and is in debt. Most of consumer finance assets and liabilities are in the form of level pay home mortgage, student, and auto loans. These products can still be tackled by the application of the Geometric series, and we can calculate various measures such as average life and time to pay a given fraction of the loan via these formulas. A large part of consumer home mortgage loans are securitized as mortgage‐backed securities by companies originally set up by the U.S. government to promote home ownership and student loans. The footprint of these giants in the financial markets is large and is the main driver of structured finance. We introduce tools and techniques to quantify the negative convexity risk due to prepayments for these markets.
While the analytical price‐yield formula for bonds, loans, and mortgage‐backed securities can provide pricing and risk measures for single products in isolation, a variety of bonds and fixed income products trade simultaneously in markets giving rise to different yield and spread curves. We introduce the bootstrap and interpolation methods to handle yields curves and overlapping cash flows of multiple instruments in a consistent manner.
Stocks, Investments
In Chapter 3, we focus on investments and the interplay between risk‐free and risky assets. We present the St. Petersburg paradox to motivate the concept of utility and to highlight the problem of investment choice, ranking, and decision‐making under uncertainty. We introduce the concept of risk‐preference and show the personalist nature of ranking of random payoffs. We present utility theory and its axioms, certainty‐equivalent lotteries, and different measures of risk‐preference (risk‐taking, risk‐aversion, risk‐neutrality) as characterized by the utility function. Utility functions representing different classes of Arrow‐Pratt measures (CARA, CRRA, HARA) are introduced and discussed.
The mean‐variance theory of portfolio selection draws from the techniques of constrained and convex optimization, and we discuss and show the method of Lagrange multipliers in various calculations such as the minimum‐variance portfolio, minimum‐variance frontier, and tangency (market) portfolio. The seminal CAPM formula relating the excess return of an asset to that of the market portfolio is derived by using the chain rule and properties of the hyperbola of feasible portfolios.
Moving from equilibrium results, we next introduce statistical techniques such as regression, factor models, and PCA to find common drivers of asset returns and statistical measures such as the alpha and beta of portfolio performance. Trading strategies such as pairs trading and mean‐reversion trades are based on these methods. We conclude by showing the use of recurrence equations and optimization techniques for risk and money management leading to the gambler's ruin formula and Kelly's ratio.
Forwards, Futures
In Chapter 4, we introduce the forward contract as the gateway product to more complicated contingent claims and options and derivatives. The basic cash‐and‐carry argument shows the method of static replication and arbitrage pricing. This method is used to compute forward prices in equities with discrete dividends or dividend yields, forward exchange rate via covered interest parity, and forward rates in interest rate markets.
Risk‐Neutral Option Pricing
Chapter 5 presents the building blocks of the modern risk‐neutral pricing framework. Starting with a simple one‐step binomial model, we flesh out the full details of the replication of a contingent claim via the underlying asset and a loan and show that a contingent claim's replication price can be computed by taking expectations in a risk‐neutral setting. This basic building block is extended to multiple steps through dynamic hedging of a self‐financing replicating portfolio, leading to martingale relative prices and the fundamental theorems of asset pricing for complete and arbitrage‐free economies.
Option Pricing
In Chapter 6, we use the risk‐neutral framework to derive the Black‐Scholes‐Merton (BSM) option pricing formula by modeling asset returns as the continuous‐time limit of a random walk, that is a Brownian motion with risk‐adjusted drift. We recover and investigate the underlying replicating portfolio by considering the option Greeks: delta, gamma, theta. The interplay between these is shown by applying the Ito's lemma to the diffusion process driving an underlying asset and its derivative, leading to the BSM partial differential equation and its solution via methods from the classical boundary value heat equations.
We discuss the Cox‐Ross‐Rubinstein (CRR) model as a popular and practical computational method for pricing options that can also be used to compute the price of options with early exercise features via the backward induction algorithm from dynamic programming. For path‐dependent options such as barrier or averaging options, we present numerical models such as the Monte Carlo simulation models and variance reduction techniques.
Interest Rate Derivatives
Chapter 7 introduces interest rate swaps and their derivatives used in structured finance. A plain vanilla swap can be priced via a static replication argument from a bootstrapped discount factor curve. In practice, simple European options on swaps and interest rate products are priced and risk‐managed via the normal version of Black's formula for futures. We introduce this model under the risk‐neutral pricing framework and show the pricing of the mainstream cap/floors, European swaptions, and CMS products. For complex derivatives, one needs a model for the evolution of multiple maturity zero‐coupon bonds in a risk‐neutral framework. We present the popular Hull‐White mean‐reverting model for the short rate and show the typical implementation methods and techniques, such as the forward induction method for yield curve inversion. We show the pricing of Bermudan swaptions via these lattice models. We conclude our discussion by presenting methods for calculating interest rate curve risk and VaR.
Exercises and Python Projects
The end‐of‐chapter exercises are based on real‐world markets and products and delve deeper into some financial products and highlight the details of applying the techniques to them. All exercises can be solved by using a spreadsheet package like Excel. The Python projects are longer problems and can be done by small groups of students as a term project.
It is my hope that by the end of this book, readers have obtained a good toolkit of mathematical techniques, methods, and models used in financial markets and products, and their interest is piqued for a deeper journey into quantitative finance.
—Amir Sadr
New York, New YorkDecember 2021
Acknowledgments
One learns by teaching and I have learned much from my students at NYU. Many thanks to all of my students over the years who have asked good questions and kept me on my toes.
Thanks to my editors at John Wiley & Sons: Bill Falloon, Purvi Patel, Samantha Enders, Julie Kerr, and Selvakumaran Rajendiran for patiently walking me through this project and correcting my many typos. All remaining errors are mine, and I welcome any corrections, suggestions, and comments sent to [email protected].
A.S.
About the Author
Amir Sadr received his PhD from Cornell University with his thesis work on the Foundations of Probability Theory. After working at AT&T Bell Laboratories, he started his Wall Street career at Morgan Stanley, initially as a Vice President in quantitative modeling and development of exotic interest rate models, and later as an exotics trader. He founded Panalytix, Inc., to develop financial software for pricing and risk management of interest rate derivatives. He was a Managing Director for proprietary trading at Greenwich Capital, Senior Trader in charge of CAD exotics and USD inflation trading at HSBC, the COO of Brevan Howard U.S. Asset Management in the United States, and co‐founder of Yield Curve Trading, a fixed income proprietary trading firm. He is currently a partner at CorePoint Partners and is focused on crypto and DeFi.
Acronyms
bp
basis points, 1% of 1%, 0.0001
future value
IRR
internal rate of return
PnL
profit and loss
present value
YTM
yield to maturity
p.a.
per annum
discount factor, today's value unit payment at future date
dicount factor at
for unit payment at
interest rate
compounding interest rate with
compoundings per year
yield
APR
annual percentage rate – stated interest rate without any compoundings
APY
annual pecentage yield – yield of a deposit taking compoundings into consideration:
for
compoundings per year
CF
cash flow
coupon rate
price of an
‐year bond with coupon rate
, paid
times per year, with yield
accrual fraction between 2 dates according to some day count basis
clean price of a bond = Price
accrued interest
price of an
‐year zero‐coupon bond with yield
,
compoundings per year
price of an
‐year annuity with annuity rate of
, paid
times per year, with yield
price of
‐maturity Treasury Bill with discount yield
PV01
present value change due to an ”01” bp change in yield
PVBP
present value change due to a 1 bp change in coupon, present value of a 1 bp annuity
balance of a level pay loan after
periods
principal and interest payments of a level pay loan in the
th period
price of
‐year level pay loan with loan rate of
, paid
times per year, with yield
AL
average life
balance of a level pay loan after
periods with prepayments
principal and interest payments of a level pay loan within the
th period with prepayments
SMM
single monthly mortality rate
CPR
constant prepayment ratio
periodic prepayment speed
utility of wealth
lottery
is preferred to
certainty‐equivalent of random payoff
,
absolute risk premium, relative risk premium
,
,
value, value of a portfolio, value of
th asset
quantity, price
weight of
th asset in a portfolio,
return of an asset over a period
:
. Can be divided by
to give rate of return
asset
's return, with mean
and standard deviation
,
C
mean vector, standard deviation vector, and covariance matrix of asset returns
return of a risk‐free asset
market portfolio, return of the market portfolio
beta of an asset
,
empirical estimate of
arithmetic average of
samples of
,
CHAPTER 1Finance
While economics as a social science studies the behavior of economic agents in the generation, acquisition, and expenditure of goods and services, finance is focused on the acquisition and management of capital in financial markets.
Focusing on the end user, finance can be divided into personal finance, corporate finance, and government finance. Savings, investments, and loans, such as credit card, student, automobile, and home mortgage, insurance products, and estate planning are examples of personal finance. The raising of capital by borrowing and debt or selling shares and equity by a company and the management of a company's funds are the focus of corporate finance. Monetary policy, central banking, tax systems, and the oversight of the banking sector and financial markets fall under government finance.
1.1 FOLLOW THE MONEY
Using the reductive definition of finance as the study of money, we follow the money to get our bearings. In accounting, a balance sheet is a snapshot of an entity's (person, corporation, country) net worth or equity: assets minus liabilities equals equity. Table 1.1 shows a snapshot of the net worth of the three dominant players in the U.S. economy: households, firms, and government.
As the table shows, households hold the largest amount of equity, followed by firms, while the U.S. government runs a negative balance and is in debt. Indeed, the U.S. government is the world's biggest borrower and routinely borrows money to finance its expenditures. The breakdown of households' net worth is shown in Table 1.2.
Bonds, stocks, foreign exchange, commodities, and their derivatives are the major sectors of financial markets. Tables 1.3 through 1.5 show the market size as of year end 2020.
TABLE 1.1 Balance sheet of the United States at 2020 year end.
Sector
Net Worth ($Trillions)
Households
123.35
Firms
33.9
Government
−26.8
Total
130.46
Source: U.S. Federal Reserve Z.1 Statistical Release.
TABLE 1.2 Households sector balance sheet as of 2020 year end.
Category
$Trillions
Percentage
Real estate
32.8
24%
Consumer durable goods
6.1
4%
Checking, savings, money market accounts
15.2
11%
Debt securities, bonds
5.1
4%
Equities, mutual funds, investments
79
57%
Misc
1.3
1%
Total assets
139.6
100%
Home mortgage loans
10.9
67%
Credit card, auto loans
4.2
26%
Other loans
1.1
7%
Total liabilities
16.2
100%
Net worth
123.35
TABLE 1.3 Market size ($Trillions).
U.S.
World
Bonds
50.1
123.5
Stocks
40.7
93.6
Derivatives
15.8
Foreign Exchange
6.6/day
Sources: World Bank, BIS, SIFMA.
TABLE 1.4 U.S. bond market ($Trillions).
Type
Outstanding debt
Treasury
21.0
42%
Mortgage‐related
11.2
22%
Corporate debt
9.8
8%
Municipal
4
8%
Federal agency securities
1.7
3%
Asset‐backed
1.5
3%
Money markets
1
2%
Total
50.1
Source: SIFMA.
TABLE 1.5 Global derivatives market size ($Trillions).
Market
Gross market value
Interest rate contracts
11.4
Foreign exchange contracts
3.2
Equity‐linked contracts
0.8
Source: BIS.
1.2 FINANCIAL MARKETS AND PARTICIPANTS
Households typically earn wages and receive salary from firms, while firms earn income when households consume their goods and services. The government collects taxes from households and firms for its expenditures for defense, government services, infrastructure, public health, and transfer payments such as social security and Medicare. Banks and financial intermediaries facilitate the transfer of funds between these three sectors: households and firms deposit their excess funds in banks and earn interest, and banks avail these funds in the form of consumer and corporate loans. Other financial intermediaries such as investment banks, insurance companies, and investment companies provide capital and financial services to firms and individuals.
The capital markets and financial instruments facilitate the flow of funds between different sectors of the economy. Focusing on the United States, the bond market is the largest market with capitalization of $50 trillion at the end of 2020. The U.S. government routinely borrows by issuing debt in the form of coupon bonds. Similarly corporations finance their growth by issuing debt in the form of corporate coupon bonds. States and municipalities also raise capital by issuing debt for infrastructure and other projects.
TABLE 1.6 Market participants and financial products.
Participant
Usage
Product
Households
Custody, banking, borrowing
Checking and interest bearing accounts, credit cards
Home mortgage, auto, student loan
Level pay loans
Investments
Cash, options brokerage accounts, financial or robo‐advisor advice for asset allocation
Insurance, estate planning
Auto, home, life insurance; annuities
Corporations
Financing
Bonds, stock issuance
Cash flow management
