An Introduction to Financial Markets E-Book

Paolo Brandimarte

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Sprache: Englisch

Seitenzahl: 1311

Veröffentlichungsjahr: 2018

Beschreibung

COVERS THE FUNDAMENTAL TOPICS IN MATHEMATICS, STATISTICS, AND FINANCIAL MANAGEMENT THAT ARE REQUIRED FOR A THOROUGH STUDY OF FINANCIAL MARKETS This comprehensive yet accessible book introduces students to financial markets and delves into more advanced material at a steady pace while providing motivating examples, poignant remarks, counterexamples, ideological clashes, and intuitive traps throughout. Tempered by real-life cases and actual market structures, An Introduction to Financial Markets: A Quantitative Approach accentuates theory through quantitative modeling whenever and wherever necessary. It focuses on the lessons learned from timely subject matter such as the impact of the recent subprime mortgage storm, the collapse of LTCM, and the harsh criticism on risk management and innovative finance. The book also provides the necessary foundations in stochastic calculus and optimization, alongside financial modeling concepts that are illustrated with relevant and hands-on examples. An Introduction to Financial Markets: A Quantitative Approach starts with a complete overview of the subject matter. It then moves on to sections covering fixed income assets, equity portfolios, derivatives, and advanced optimization models. This book's balanced and broad view of the state-of-the-art in financial decision-making helps provide readers with all the background and modeling tools needed to make "honest money" and, in the process, to become a sound professional. * Stresses that gut feelings are not always sufficient and that "critical thinking" and real world applications are appropriate when dealing with complex social systems involving multiple players with conflicting incentives * Features a related website that contains a solution manual for end-of-chapter problems * Written in a modular style for tailored classroom use * Bridges a gap for business and engineering students who are familiar with the problems involved, but are less familiar with the methodologies needed to make smart decisions An Introduction to Financial Markets: A Quantitative Approach offers a balance between the need to illustrate mathematics in action and the need to understand the real life context. It is an ideal text for a first course in financial markets or investments for business, economic, statistics, engi-neering, decision science, and management science students.

Leseprobe

An Introduction to Financial Markets

A Quantitative Approach

Paolo Brandimarte

This edition first published 2018 © 2018 John Wiley & Sons, Inc.

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Library of Congress Cataloging-in-Publication Data

ISBN: 978-1-118-01477-6

Contents

Preface

About the Companion Website

Part One Overview

Chapter One Financial Markets: Functions, Institutions, and Traded Assets

1.1 What is the purpose of finance?

1.2 Traded assets

1.3 Market participants and their roles

1.4 Market structure and trading strategies

1.5 Market indexes

Problems

Further reading

Bibliography

Notes

Chapter Two Basic Problems in Quantitative Finance

2.1 Portfolio optimization

2.2 Risk measurement and management

2.3 The no-arbitrage principle in asset pricing

2.4 The mathematics of arbitrage

S2.1 Multiobjective optimization

S2.2 Summary of LP duality

Problems

Further reading

Bibliography

Notes

Part Two Fixed-income assets

Chapter Three Elementary Theory of Interest Rates

3.1 The time value of money: Shifting money forward in time

3.2 The time value of money: Shifting money backward in time

3.3 Nominal vs. real interest rates

3.4 The term structure of interest rates

3.5 Elementary bond pricing

3.6 A digression: Elementary investment analysis

3.7 Spot vs. forward interest rates

Problems

Further reading

Bibliography

Notes

Chapter Four Forward Rate Agreements, Interest Rate Futures, and Vanilla Swaps

4.1 LIBOR and EURIBOR rates

4.2 Forward rate agreements

4.3 Eurodollar futures

4.4 Vanilla interest rate swaps

Problems

Further reading

Bibliography

Notes

Chapter Five Fixed-Income Markets

5.1 Day count conventions

5.2 Bond markets

5.3 Interest rate derivatives

5.4 The repo market and other money market instruments

5.5 Securitization

Problems

Further reading

Bibliography

Notes

Chapter Six Interest Rate Risk Management

6.1 Duration as a first-order sensitivity measure

6.2 Further interpretations of duration

6.3 Classical duration-based immunization

6.4 Immunization by interest rate derivatives

6.5 A second-order refinement: Convexity

6.6 Multifactor models in interest rate risk management

Problems

Further reading

Bibliography

Notes

Part Three Equity portfolios

Chapter Seven Decision-Making under Uncertainty: The Static Case

7.1 Introductory examples

7.2 Should we just consider expected values of returns and monetary outcomes?

7.3 A conceptual tool: The utility function

7.4 Mean-risk models

7.5 Stochastic dominance

S7.1 Theorem proofs

Problems

Further reading

Bibliography

Notes

Chapter Eight Mean–Variance Efficient Portfolios

8.1 Risk aversion and capital allocation to risky assets

8.2 The mean-variance efficient frontier with risky assets

8.3 Mean–variance efficiency with a risk-free asset: The separation property

8.4 Maximizing the Sharpe ratio

8.5 Mean–variance efficiency vs. expected utility

8.6 Instability in mean–variance portfolio optimization

S8.1 The attainable set for two risky assets is a hyperbola

S8.2 Explicit solution of mean–variance optimization in matrix form

Problems

Further reading

Bibliography

Notes

Chapter Nine Factor Models

9.1 Statistical issues in mean-variance portfolio optimization

9.2 The single-index model

9.3 The Treynor-Black model

9.4 Multifactor models

9.5 Factor models in practice

S9.1 Proof of Equation (9.17)

Problems

Further reading

Bibliography

Notes

Chapter Ten Equilibrium Models: CAPM and APT

10.1 What is an equilibrium model?

10.2 The capital asset pricing model

10.3 The Black-Litterman portfolio optimization model

10.4 Arbitrage pricing theory

10.5 The behavioral critique

S10.1 Bayesian statistics

Problems

Further reading

Bibliography

Notes

Part Four Derivatives

Chapter Eleven Modeling Dynamic Uncertainty

11.1 Stochastic processes

11.2 Stochastic processes in continuous time

11.3 Stochastic differential equations

11.4 Stochastic integration and Itô’s lemma

11.5 Stochastic processes in financial modeling

11.5.1 Geometric Brownian Motion

11.5.2 Generalizations

11.6 Sample path generation

S11.1 Probability spaces, measurability, and information

Problems

Further reading

Bibliography

Notes

Chapter Twelve Forward and Futures Contracts

12.1 Pricing forward contracts on equity and foreign currencies

12.2 Forward vs. futures contracts

12.3 Hedging with linear contracts

Problems

Further reading

Bibliography

Notes

Chapter Thirteen Option Pricing: Complete Markets

13.1 Option terminology

13.2 Model-free price restrictions

13.3 Binomial option pricing

13.4 A continuous-time model: The Black–Scholes–Merton pricing formula

13.5 Option price sensitivities: The Greeks

13.6 The role of volatility

13.7 Options on assets providing income

13.8 Portfolio strategies based on options

13.9 Option pricing by numerical methods

Problems

13.12 Further reading

Bibliography

Notes

Chapter Fourteen Option Pricing: Incomplete Markets

14.1 A PDE approach to incomplete markets

14.2 Pricing by short-rate models

14.3 A martingale approach to incomplete markets

14.4 Issues in model calibration

Further reading

Bibliography

Notes

Part Five Advanced optimization models

Chapter Fifteen Optimization Model Building

15.1 Classification of optimization models

15.2 Linear programming

15.3 Quadratic programming

15.4 Integer programming

15.5 Conic optimization

15.6 Stochastic optimization

15.7 Stochastic dynamic programming

15.8 Decision rules for multistage SLPs

15.9 Worst-case robust models

15.10 Nonlinear programming models in finance

Problems

Further reading

Bibliography

Notes

Chapter Sixteen Optimization Model Solving

16.1 Local methods for nonlinear programming

16.2 Global methods for nonlinear programming

16.3 Linear programming

16.4 Conic duality and interior-point methods

16.5 Branch-and-bound methods for integer programming

16.6 Optimization software

Problems

Further reading

Bibliography

Notes

Index

EULA

List of Table

Chapter 1

Table 1.1

Table 1.2

Table 1.3

Table 1.4

Chapter 2

Table 2.1

Table 2.2

Table 2.3

Table 2.4

Chapter 3

Table 3.1

Table 3.2

Table 3.3

Table 3.4

Table 3.5

Table 3.6

Chapter 4

Table 4.1

Table 4.2

Table 4.3

Chapter 7

Table 7.1

Table 7.2

Table 7.3

Chapter 8

Table 8.1

Chapter 10

Table 10.1

Table 10.2

Table 10.3

Chapter 13

Table 13.1

Table 13.2

Chapter 15

Table 15.1

Guide

Cover

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E-1

Preface

This book arises from slides and lecture notes that I have used over the years in my courses Financial Markets and Instruments and Financial Engineering, which were offered at Politecnico di Torino to graduate students in Mathematical Engineering. Given the audience, the treatment is naturally geared toward a mathematically inclined reader. Nevertheless, the required prerequisites are relatively modest, and any student in engineering, mathematics, and statistics should be well-equipped to tackle the contents of this introductory book.1 The book should also be of interest to students in economics, as well as junior practitioners with a suitable quantitative background.

We begin with quite elementary concepts, and material is introduced progressively, always paying due attention to the practical side of things. Mathematical modeling is an art of selective simplification, which must be supported by intuition building, as well as by a healthy dose of skepticism. This is the aim of remarks, counterexamples, and financial horror stories that the book is interspersed with. Occasionally, we also touch upon current research topics.

Book structure

The book is organized into five parts.

Part One,

Overview

, consists of two chapters. Chapter 1 aims at getting unfamiliar readers acquainted with the role and structure of financial markets, the main classes of traded assets (equity, fixed income, and derivatives), and the main types of market participants, both in terms of institutions (e.g., investments banks and pension funds) and roles (e.g., speculators, hedgers, and arbitrageurs). We try to give a practical flavor that is essential to students of quantitative disciplines, setting the stage for the application of quantitative models. Chapter 2 overviews the basic problems in finance, like asset allocation, pricing, and risk management, which may be tackled by quantitative models. We also introduce the fundamental concepts related to arbitrage theory, including market completeness and risk-neutral measures, in a simple static and discrete setting.

Part Two,

Fixed-income assets

, consists of four chapters and introduces the simplest assets depending on interest rates, starting with plain bonds. The fundamental concepts of interest rate modeling, including the term structure and forward rates, as well as bond pricing, are covered in Chapter 3. The simplest interest rate derivatives (forward rate agreements and vanilla swaps) are covered in Chapter 4, whereas Chapter 5 aims at providing the reader with a flavor of real-life markets, where details like day count and quoting conventions are relevant. Chapter 6 concludes this part by showing how quantitative models may be used to manage interest rate risk. In this part, we do not consider interest rate options, which require a stronger mathematical background and are discussed later.

Part Three,

Equity portfolios

, consists of four chapters, where we discuss equity markets and portfolios of stock shares. Actually, this is not the largest financial market, but it is arguably the kind of market that the layman is more familiar with. Chapter 7 is a bit more theoretical and lays down the foundations of static decision-making under uncertainty. By static, we mean that we make one decision and then we wait for its consequences, finger crossed. Multistage decision models are discussed later. In this chapter, we also introduce the basics of risk aversion and risk measurement. Chapter 8 is quite classical and covers traditional meanr-variance portfolio optimization. The impact of statistical estimation issues on portfolio management motivates the introduction of factor models, which are the subject of Chapter 9. Finally, in Chapter 10, we discuss equilibrium models in their simplest forms, the capital asset pricing model (CAPM), which is related to a single-index factor model, and arbitrage pricing theory (APT), which is related to a multifactor model. We do not discuss further developments in equilibrium models, but we hint at some criticism based on behavioral finance.

Part Four,

Derivatives

, includes four chapters. We discuss dynamic uncertainty models in Chapter 11, which is more challenging than previous chapters, as we have to introduce the necessary foundations of option pricing models, namely, stochastic differential equations and stochastic integrals. Chapter 12 describes simple forward and futures contracts, extending concepts that were introduced in Chapter 4, when dealing with forward and futures interest rates. Chapter 13 covers option pricing in the case of complete markets, including the celebrated and controversial Black-Scholes-Merton formula, whereas Chapter 14 extends the basic concepts to the more realistic setting of incomplete markets.

Part Five,

Advanced optimization models

, is probably the less standard part of this book, when compared to typical textbooks on financial markets. We deal with optimization model building, in Chapter 15, and optimization model solving, in Chapter 16. Actually, it is difficult to draw a sharp line between model building and model solving, but it is a fact of life that advanced software is available for solving quite sophisticated models, and the average user does not need a very deep knowledge of the involved algorithms, whereas she must be able to build a model. This is the motivation for separating the two chapters.

Needless to say, the choice of which topics should be included or omitted is debatable and based on authorsr’ personal bias, not to mention the need to keep a book size within a sensible limit. With respect to introductory textbooks on financial markets, there is a deeper treatment of derivative models. On the other hand, more challenging financial engineering textbooks do not cover, e.g., equilibrium models and portfolio optimization. We aim at an intermediate treatment, whose main limitations include the following:

We only hint at criticism put forward by behavioral finance and do not cover market microstructure and algorithmic trading strategies.

From a mathematical viewpoint, we pursue an intuitive treatment of financial engineering models, as well as a simplified coverage of the related tools of stochastic calculus. We do not rely on rigorous arguments involving self-financing strategies, martingale representation theorems, or change of probability measures.

From a financial viewpoint, by far, the most significant omission concerns credit risk and credit derivatives. Counterparty and liquidity risk play a prominent role in post-Lehman Brothers financial markets and, as a consequence of the credit crunch started in 2007, new concepts like CVA, DVA, and FVA have been introduced. This is still a field in flux, and the matter is arguably not quite assessed yet.

Another major omission is econometric time series models.

Adequate references on these topics are provided for the benefit of the interested readers.

My choices are also influenced by the kind of students this book is mainly aimed at. The coverage of optimization models and methods is deeper than usual, and I try to open readers’ critical eye by carefully crafted examples and counterexamples. I try to strike a satisfactory balance between the need to illustrate mathematics in action and the need to understand the real-life context, without which quantitative methods boil down to a solution in search of a problem (or a hammer looking for nails, if you prefer). I also do not disdain just a bit of repetition and redundancy, when it may be convenient to readers who wish to jump from chapter to chapter. More advanced sections, which may be safely skipped by readers, are referred to as supplements and their number is marked by an initial “S.”

In my Financial Engineering course, I also give some more information on numerical methods. The interested reader might refer to my other books:

P. Brandimarte,

Numerical Methods in Finance and Economics: A MAT-LAB-Based Introduction

(2nd ed.), Wiley, 2006

P. Brandimarte,

Handbook in Monte Carlo Simulation:Applications in Financial Engineering, Risk Management, and Economics

, Wiley, 2014

Acknowledgements

In the past years, I have adopted the following textbooks (or earlier editions) in my courses. I have learned a lot from them, and they have definitely influenced the writing of this book:

Z. Bodie, A. Kane, and A. Marcus,

Investments

(9th ed.), McGraw-Hill, 2010

J.C. Hull, Options,

Futures, and Other Derivatives

(8th ed.), Prentice Hall, 2011

P. Veronesi,

Fixed Income Securities: Valuation, Risk, and Risk Management

, Wiley, 2010

Other specific acknowledgements are given in the text. I apologize in advance for any unintentional omission.

Additional material

Some end-of-chapter problems are included and fully worked solutions will be posted on a web page. My current URL is

http://staff.polito.it/paolo.brandimarte/

A hopefully short list of errata will be posted there as well. One of the many corollaries of Murphy’s law states that my URL is going to change shortly after publication of the book. An up-to-date link will be maintained on the Wiley web page:

http://www.wiley.com/

For comments, suggestions, and criticisms, all of which are quite welcome, my e-mail address is

[email protected]

PAOLO BRANDIMARTE

Turin, September 2017

Note

1

  In case of need, the mathematical prerequisites are covered in my other book:

Quantitative Methods: An Introduction for Business Management

. Wiley, 2011.

About the Companion Website

This book is accompanied by a companion website:

www.wiley.com/go/brandimarte/financialmarkets

The website includes:

Solutions manual for end-of-chapter problems

Part OneOverview