Cover
Introduction
1. Why You Should Read This Book
2. The Intended Reader
3. Why MATLAB®?
4. How to Use This Book
5. Font Conventions
6. About the Author
7. MathWorks Information
8. References
PART I: MATLAB Conventions and Basic Skills
1. CHAPTER 1: Working with MATLAB® Data
  1. 1.1 Introduction
  2. 1.2 Arrays
  3. 1.3 Character Arrays
  4. 1.4 Flexible Data Structures
  5. References
  6. Further Reading
2. CHAPTER 2: Working with Dates and Times
  1. 2.1 Introduction
  2. 2.2 Finance Background: Why Dates and Times Matter
  3. 2.3 Dates and Times in MATLAB
  4. References
  5. Notes
3. CHAPTER 3: Basic Programming with MATLAB®
  1. 3.1 Introduction
  2. 3.2 MATLAB Scripts and Functions
  3. References
4. CHAPTER 4: Working with Financial Data
  1. 4.1 Introduction
  2. 4.2 Accessing Financial Data
  3. 4.3 Working with Spreadsheet Data
  4. 4.4 Data Visualization
  5. References
PART II: Financial Calculations with MATLAB
1. CHAPTER 5: The Time Value of Money
  1. 5.1 Introduction
  2. 5.2 Finance Background
  3. 5.3 MATLAB Time Value of Money Functions
  4. 5.4 Internal Rate of Return
  5. 5.5 Effective Interest Rates
  6. 5.6 Compound Annual Growth Rate
  7. 5.7 Continuous Interest
  8. 5.8 Loans
  9. References
2. CHAPTER 6: Bonds
  1. 6.1 Introduction
  2. 6.2 Finance Background
  3. 6.3 MATLAB Bond Functions
  4. 6.4 Bond Analytics
  5. 6.5 Callable Bonds
  6. References
  7. Further Reading
  8. Note
3. CHAPTER 7: Dealing with Uncertainty and Risk
  1. 7.1 Introduction
  2. 7.2 Overview of Financial Risk
  3. 7.3 Data Insights
  4. 7.4 Data Relationships
  5. 7.5 Creating a Basic Simulation Model
  6. 7.6 Value at Risk (VaR)
  7. References
  8. Further Reading
  9. Notes
4. CHAPTER 8: Equity Derivatives
  1. 8.1 Introduction
  2. 8.2 Options
  3. 8.3 Option Pricing Models
  4. 8.4 Options' Uses
  5. 8.5 Appendix: Other Types of Derivatives
  6. References
  7. Further Reading
  8. Note
5. CHAPTER 9: Portfolios
  1. 9.1 Introduction
  2. 9.2 Finance Background
  3. 9.3 Portfolio Optimization
  4. 9.4 MATLAB Portfolio Object
  5. References
6. CHAPTER 10: Regression and Time Series
  1. 10.1 Introduction
  2. 10.2 Basic Regression
  3. 10.3 Working with Time Series
  4. References
APPENDIX 1: Sharing Your Work
1. A1.1 Introduction
2. A1.2 Publishing a Script
3. References
APPENDIX 2: Reference for Included MATLAB® Functions
Index
End User License Agreement

List of Tables

Chapter 1
1. Table 1.1 MATLAB Data Terminology
2. Table 1.2 MATLAB Array Types
3. Table 1.3 Functions that Create Vectors
4. Table 1.4 Functions that Generate Random Numbers
5. Table 1.5 Common Scalar Operations
6. Table 1.6 Row-column Compatibility
7. Table 1.7 Correlation Coefficients for Stocks, Bills, and Bonds
8. Table 1.8 Row and Column Index Reference Values
9. Table 1.9 Relational Operators
10. Table 1.10 Logical Operators and Functions
11. Table 1.11 Stock Data
Chapter 2
1. Table 2.1 Common Day-Count Methods
2. Table 2.2 Date and Time Variables
3. Table 2.3 Common Datetime Identifiers
4. Table 2.4 Serial Date Conversion Functions
5. Table 2.5 Calculating Time Between Dates
6. Table 2.6 Elapsed Time Functions for Different Date Formats
Chapter 4
1. Table 4.1 Built-in Financial Charts
Chapter 5
1. Table 5.1 Simple Interest Calculation
2. Table 5.2 Simple Interest Period Adjustments
3. Table 5.3 Compound Interest
4. Table 5.4 Compound Interest Formula Derivation
5. Table 5.5 Future Value of Unequal Cash Flows
6. Table 5.6 Future Value of Equal Cash Flows
7. Table 5.7 Present Value Formulas
8. Table 5.8 Year-End Investment Values
Chapter 6
1. Table 6.1 Bond Classifications
2. Table 6.2 Bond Terms
3. Table 6.3 Bond Usage Abbreviations
4. Table 6.4 Bndprice Function Arguments
5. Table 6.5 Percentage Change in Price with Interest Rate Changes
6. Table 6.6 US Treasury Rates
Chapter 7
1. Table 7.1 Covariance Table Interpretation
2. Table 7.2 Correlation Table Interpretation
Chapter 8
1. Table 8.1 Fundamental Option Terms
2. Table 8.2 Intrinsic Value Versus Option Price
3. Table 8.3 Replicated Portfolio Terminal Value
4. Table 8.4 Binprice Function
5. Table 8.5 The Greeks
6. Table 8.6 The Greeks' Syntax
7. Table 8.7 Comparative Profits
8. Table 8.8 Option Spreads
9. Table 8.9 MATLAB Supported Exotic Options
Chapter 9
1. Table 9.1 Unconstrained Portfolio Weights
2. Table 9.2 Constrained Portfolio Weights
3. Table 9.3 Optimal Unconstrained Allocations for Target Returns

List of Illustrations

Chapter 1
1. Figure 1.1 Variables Listed in Workspace Window
2. Figure 1.2 Data Import Options
3. Figure 1.3 10-Year Treasury Yields 1998–2017
4. Figure 1.4 Plotting with Missing Data
5. Figure 1.5 Filling Missing Data With Estimated Value
6. Figure 1.6 Variable Data Editor
7. Figure 1.7 Reviewing Data Cells
8. Figure 1.8 Structure Data Fields
9. Figure 1.9 CSV Data Format
10. Figure 1.10 Microsoft Excel File Format
11. Figure 1.11 Import Data Tool
12. Figure 1.12 Imported Data
13. Figure 1.13 Data Import Options
Chapter 2
1. Figure 2.1 Import Tool
2. Figure 2.2 Import Date Formats
3. Figure 2.3 Custom Date Format Field
4. Figure 2.4 Dates Converted to Datetime Format
5. Figure 2.5 Imported Table
6. Figure 2.6 Date Conversion in Microsoft Excel
7. Figure 2.7 x2mdate Excel to MATLAB Conversion
8. Figure 2.8 Microsoft Excel Dates in MATLAB
9. Figure 2.9 Plotting with Datetime Variables
Chapter 3
1. Figure 3.1 Editor Toolbar
2. Figure 3.2 Future Value Script
3. Figure 3.3 Set Path Dialog Box
4. Figure 3.4 Function Template
5. Figure 3.5 futureValueCalc Function
6. Figure 3.6 futureValueCalc Help Screen
7. Figure 3.7 Input Prompt
8. Figure 3.8 Input Request
9. Figure 3.9 Warning Dialog Box
10. Figure 3.10 Error Dialog Box
11. Figure 3.11 Input Problem Box
12. Figure 3.12 Potential Error Highlights
13. Figure 3.13 Possible Error Correction
14. Figure 3.14 Code Improvement Suggestion
Chapter 4
1. Figure 4.1 Google Finance Download
2. Figure 4.2 Yahoo! Finance Download
3. Figure 4.3 10-Year Bond Rate
4. Figure 4.4 Data Import Tool
5. Figure 4.5 Import Tool Data Display
6. Figure 4.6 Importing Datetime Variables
7. Figure 4.7 Specifying Data Types
8. Figure 4.8 Importing Selected Variables
9. Figure 4.9 Full Import Tab
10. Figure 4.10 Data Import to Table
11. Figure 4.11 Variables Window Data View
12. Figure 4.12 Imported FRED Data
13. Figure 4.13 Import Selection Options
14. Figure 4.14 Data Import Problem
15. Figure 4.15 Corrected Data Import
16. Figure 4.16 Importing Data to Column Vectors
17. Figure 4.17 Data Imported as Column Vectors
18. Figure 4.18 Attempted Import as Matrix
19. Figure 4.19 Date Data Fails to Import
20. Figure 4.20 Downloaded FRED Data
21. Figure 4.21 Spreadsheet Data Import
22. Figure 4.22 Selected Workspace Variables
23. Figure 4.23 Plots Tab
24. Figure 4.24 Apple Close Price
25. Figure 4.25 AAPL and IBM Plot
26. Figure 4.26 Show Plot Tools Icon
27. Figure 4.27 Plot Property Editor Dialogue Box
28. Figure 4.28 AAPL and IBM Prices
29. Figure 4.29 Dates Displayed as Serial Dates
30. Figure 4.30 Dates with DatetimeTickFormat Argument
31. Figure 4.31 Series Comparison with a Single y-axis
32. Figure 4.32 Data Plot with Double y-axes
33. Figure 4.33 Single Data Series in Single Figure
34. Figure 4.34 2 × 1 Array of Blank Plots
35. Figure 4.35 Two Data Series in Two Plots
36. Figure 4.36 Property Editor Display Name
37. Figure 4.37 Insert Legend Icon
38. Figure 4.38 Legend Locator
39. Figure 4.39 Adding Text to Plot
40. Figure 4.40 Surface Plot
41. Figure 4.41 Hi-Lo-Close Plot for AAPL
42. Figure 4.42 Candlestick Plot for AAPL
Chapter 6
1. Figure 6.1 Normal Yield Curve
Chapter 7
1. Figure 7.1 Historical Asset Returns Excel Worksheet
2. Figure 7.2 MATLAB Import Screen
3. Figure 7.3 MATLAB Workspace after Data Import
4. Figure 7.4 Annualized S&P 500 Returns
5. Figure 7.5 Treasury Bills vs. Treasury Bonds, 1928 to 2016
6. Figure 7.6 Histogram of S&P 500 Annual Returns
7. Figure 7.7 Histogram of S&P 500 Annual Returns (12 Bins)
8. Figure 7.8 Histogram of Treasury Bond Annual Returns (12 Bins)
9. Figure 7.9 Histfit of Normal(5,1) Distribution
10. Figure 7.10 HIsfit of Normal(5,1) Distribution with 10,000 Points
11. Figure 7.11 S&P 500 Returns Versus Normal Distribution
12. Figure 7.12 T-bond Returns Versus Normal Distribution
13. Figure 7.13 Probplot with Normal(5,1) Random Data
14. Figure 7.14 Probplot for S&P 500 Data
15. Figure 7.15 AMZN Daily Close Price 2015–2016
16. Figure 7.16 Simulated 10-Day Amazon Price Paths
17. Figure 7.17 Simulated Returns for Normal (12,20) Distribution
18. Figure 7.18 Simulated Returns with VaR Levels
Chapter 8
1. Figure 8.1 CBOE Price Data for AAPL
Chapter 9
1. Figure 9.1 Three-asset Class Efficient Frontier
2. Figure 9.2 Imported Stock Data
3. Figure 9.3 Returns Data
4. Figure 9.4 Portfolio Object Efficient Frontier
5. Figure 9.5 Optimal Portfolio
Chapter 10
1. Figure 10.1 Scatterplot of Consumer Confidence Versus Durable Goods Orders
2. Figure 10.2 Scatterplot of Consumer Confidence Versus Durable Goods Orders with Line
3. Figure 10.3 Fitting a Straight Line to a Curve
4. Figure 10.4 Fitted Curve Comparisons
5. Figure 10.5 Fitting a Line with polyfit
6. Figure 10.6 Plot Function Output
7. Figure 10.7 Histogram of Model Residuals
8. Figure 10.8 FTS Icon in the Apps Menu
9. Figure 10.9 FTS Dialog Box with Data Loaded
10. Figure 10.10 Access the FTSGUI Tools
11. Figure 10.11 FTS Data Tools
12. Figure 10.12 FTS Technical Analysis Tools
13. Figure 10.13 FTS Graphs Tools
14. Figure 10.14 File Load for FTSGUI
15. Figure 10.15 Basic AMZN Close Price Line Plot with Volume
APPENDIX 1
1. Figure A1.1 Publishing Tool Strip
2. Figure A1.2 Publish Options
3. Figure A1.3 Edit Configurations Dialog Box
4. Figure A1.4 Output File Format Options
5. Figure A1.5 HTML Output Format
6. Figure A1.6 Creating a Live Script
7. Figure A1.7 Live Editor Tool Strip
8. Figure A1.8 Live Script Inputs
9. Figure A1.9 Live Script Options
10. Figure A1.10 Live Script Two-Column Format
11. Figure A1.11 Live Script Figure Output
12. Figure A1.12 Equation Menu
13. Figure A1.13 Live Script Inserted Equation

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MATLAB® is a trademark of The MathWorks, Inc. and is used with permission. The MathWorks does not warrant the accuracy of the text or exercises in this book. This work's use or discussion of MATLAB® software or related products does not constitute endorsement or sponsorship by The MathWorks of a particular pedagogical approach or particular use of the MATLAB® software. While the publisher and authors have used their best efforts in preparing this work, they make no representations or warranties with respect to the accuracy or completeness of the contents of this work and specifically disclaim all warranties, including without limitation any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives, written sales materials or promotional statements for this work. The fact that an organization, website, or product is referred to in this work as a citation and/or potential source of further information does not mean that the publisher and authors endorse the information or services the organization, website, or product may provide or recommendations it may make. This work is sold with the understanding that the publisher is not engaged in rendering professional services. The advice and strategies contained herein may not be suitable for your situation. You should consult with a specialist 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.

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Library of Congress Cataloging-in-Publication Data

Names: McCarthy, Ed (Edward), 1955– author.

Title: Foundations of computational finance with MATLAB / by Ed McCarthy.

Description: Hoboken, New Jersey : John Wiley & Sons, Inc., [2018] | Includes index. |

Identifiers: LCCN 2018014808 (print) | LCCN 2018016054 (ebook) | ISBN 9781119433873 (epub) | ISBN 9781119433910 (pdf) | ISBN 9781119433859 (cloth)

Subjects: LCSH: Finance—Mathematical models. | Finance—Data processing.

Classification: LCC HG106 (ebook) | LCC HG106 .M396 2018 (print) | DDC 332.0285/53—dc23

LC record available at https://lccn.loc.gov/2018014808

Cover Design: Wiley

Cover Image: © monsitj/iStockphoto

Introduction

Why You Should Read This Book

If you're planning a career in corporate or investment finance or already working in one of those areas, you're probably proficient with financial calculators and spreadsheets. Those technologies have proven their value, and it's likely they will remain essential tools for many years. (I still use a 30-year-old Hewlett Packard 12C calculator regularly and it works perfectly, albeit a bit slower than newer models.)

But the nature of data and analytics are changing, and those changes are influencing financial analysis and management. Traditional financial data still drive decisions, but those data are being supplemented by increasing volumes of nontraditional information and new computational tools. Consider these headlines from recent years, which are just a small sample of the articles on these themes:

“Stop Using Excel, Finance Chiefs Tell Staffs” (Wall Street Journal, 1/22/1017)
“The Quants Run Wall Street Now” (Wall Street Journal, article series in May 2017)
“At New Digital Lenders, Math Rules” (New York Times, 1/19/2016)
“Leveraging Data to Own the Engaged Customer” (Utility Analytics, 11/4/2015)
“The Morning Ledger: The Rising Profile of Financial Planning and Analysis” (Wall Street Journal, 12/22/2015)
“How Computers Trawl a Sea of Data for Stock Picks” (Wall Street Journal, 4/1/2015)
“As Big Data and AI Take Hold, What Will It Take to Be an Effective Executive?” (Wall Street Journal, 1/23/2015)

I believe this paradigm shift requires a new approach to financial analysis and management. Specifically, finance professionals must supplement their calculators and spreadsheets with more flexible and powerful computational platforms. These platforms can work with the new data models while still providing the tools needed for traditional financial analysis. As the headlines suggest, remaining competitive in financial analysis and management will require an understanding of and skill with computational finance. This knowledge will allow you to access data from multiple sources, develop customized financial analytics, and then distribute your tools and findings across a variety of platforms.

The Intended Reader

Transitioning to the new paradigm is a challenge, though, because it means learning about computational finance. Other authors have addressed this topic, but they focused on advanced material for readers who combine extensive math, statistics, programming, and finance backgrounds, such as financial engineers and academics.

In contrast, I wrote this book for readers seeking an introductory text that links traditional finance material to the MATLAB computational platform. This includes upper-level undergraduate finance students, graduate students, finance practitioners, and those with STEM backgrounds seeking to learn about finance. My assumption is that your background will be: (1) A business student or finance professional who is comfortable with finance theory but has modest computer programming experience beyond spreadsheets, or (2) A STEM student or professional who has a more extensive programming background but less experience with finance.

I'm also assuming you have completed first courses in linear algebra and statistics and will have access to MATLAB and the required MATLAB Toolboxes. Many universities have MATLAB licenses, but if you must buy the software, it's very inexpensive for students, and the MATLAB Home edition makes it readily affordable for nonacademic users. (Pricing details are available on the mathworks.com site.)

Why MATLAB®?

That's a fair question, because there are a host of programming languages being used in finance. But there's a question-and-answer dialogue I've seen numerous times on web message boards for quantitative and computational finance that helps answer the question. It goes something like this:

Q. I'm thinking of getting into quantitative finance (or applying to a quant educational program) and need advice on programming languages. Should I start with MATLAB or Python? R or S? C++ or Java?

A. Yes.

The answer is a bit snarky, so the respondent usually explains that learning a programming language is not a one-and-done lifetime proposition. People change employers during their careers and the new employer might emphasize a different language. Computer technologies and programming languages evolve, too, and it's necessary to keep up with those changes, as those of us who started programming with punched cards and card readers can attest.

I have no business affiliation with The MathWorks but I believe the MATLAB software is well-suited for an introduction to computational finance for several reasons:

It's an integrated development environment that combines a code editor, compiler, debugger, interpreter, and graphics capability in a well-designed graphical user interface.
It's relatively easy to develop basic MATLAB skills. Of course, it takes time and effort to learn any computer language but the program's consistent syntax usage and extensive documentation improve user productivity.
The finance-related MATLAB Toolboxes provide access to multiple financial functions running tested algorithms, which can save many programming hours and much frustration. Additional MATLAB Toolboxes can make it easier to move into other areas, such as big data analytics, as well.
MATLAB is used in numerous financial firms, other industries, and over 5,000 universities. If you're a student, your school probably has a MATLAB license.
Prices for students and educators have always been low, and several years ago The MathWorks began offering inexpensive personal licenses.
Users can access multiple training and support channels through general and specialized books, online and live training courses, and formal and informal (community) support resources. I've completed several of the online training programs offered by The MathWorks, and they were very good.
Finally, I believe the knowledge and skills developed in learning MATLAB make it easier to subsequently learn other programming languages.

How to Use This Book

Part I introduces the MATLAB syntax and how to use the program. If you're new to MATLAB or need a review, start with those chapters. For a deeper introduction, you can supplement that material with the resources online The MathWorks offers, including the no-cost MATLAB Onramp course at matlabacademy.mathworks.com. That course uses an interactive format and takes about two hours to complete. Other online tutorials can be found at www.mathworks.com/support/learn-with-matlab-tutorials.html. If you have the time and funds, the MATLAB Fundamentals course is an excellent in-depth introduction.

Part II demonstrates how MATLAB can be used as a computational platform in finance. The material in Chapter 5, “The Time Value of Money,” has general applications throughout the remaining chapters, so I suggest reviewing that material. The text reviews the underlying finance material being discussed in each chapter and includes suggestions for further reading.

Finally, practice using the program interactively or programmatically by entering commands in the MATLAB Command window as you work through the examples. Learning to use software is somewhat like learning to drive. Reading a book on safe driving gives you an intellectual perspective but it makes driving sound deceptively easy. Coding—like getting behind the steering wheel and pulling into high-speed traffic for the first time—is best experienced hands-on. Fortunately, writing code is a lot less nerve-wracking than highway driving.

Font Conventions

The book uses several different font styles to help you distinguish the material:

Bold: Function names, reserved keywords, matrices, and vectors

Monospaced italic: Command window inputs. Example:

x = 7

Monospaced: MATLAB output and responses. Example:

x =
     7

Monospaced starting with %: Code comment lines that do not execute

Normally spaced lines starting with %: Text comments

About the Author

I have worked as a freelance finance writer since the mid-1980s, and during that time I have written for many of the financial service industry's leading publications. These include Bloomberg Wealth Manager, CFA Institute Magazine, Institutional Investor online, Financial Planning, Journal of Accountancy, and the Journal of Financial Planning. Earlier in my career I published a technology book for financial advisors, The Financial Advisor's Analytical Toolbox (Irwin), and one for consumers, Fast Forward MBA in Personal Finance (Wiley). I have also written numerous print and web articles for custom publishers and many of the largest U.S. and international financial services firms. My primary experience as a writer and the focus for many of my articles has been explaining complex finance topics and technologies to readers.

My first exposure to MATLAB was in the mid-1990s when I was doing research for my first book, which included a discussion of the software's financial modeling capabilities. My use of the program intensified while I was studying for a PhD in finance, and I believe my experience at that time supports the premise for this book. The lack of available resources to link finance theory with the requisite computer programming made that aspect of the work more difficult than it needed to be. I chose not to finish my dissertation and left school to write full-time, but I continued to use the software and periodically work through new financial mathematics and MATLAB texts to stay current. I am a MathWorks Certified MATLAB Associate and am working toward The MathWorks Certified MATLAB Professional designation.

MathWorks Information

The material in this book was developed using the MATLAB R2016B, 2017A, and 2017B releases and MATLAB Toolboxes for the same releases.

For MATLAB and Simulink product information, please contact:

The MathWorks, Inc.
3 Apple Hill Drive
Natick, MA, 01760-2098 USA Tel: 508-647-7000
Fax: 508-647-7001
E-mail: info@mathworks.com
Web: mathworks.com
How to buy: www.mathworks.com/store

References

Hope, Bradley. “How Computers Trawl a Sea of Data for Stock Picks.” Wall Street Journal, April 1, 2015. Accessed January 15, 2016. https://www.wsj.com/articles/how-computers-trawl-a-sea-of-data-for-stock-picks-1427941801.
Lohr, Steve. “At New Digital Lenders, Math Rules.” New York Times, January 19, 2016. Accessed January 20, 2016. https://bits.blogs.nytimes.com/2016/01/19/at-new-digital-lenders-math-rules/.
Shumsky, Tatyana. “Stop Using Excel, Finance Chiefs Tell Staffs.” Wall Street Journal, January 22, 2017. Accessed January 22, 2017. https://www.wsj.com/articles/stop-using-excel-finance-chiefs-tell-staffs-1511346601.
Willhite, James. “The Morning Ledger: The Rising Profile of Financial Planning and Analysis.” Wall Street Journal, December 22, 2015. Accessed January 15, 2016. https://blogs.wsj.com/cfo/2015/12/22/the-morning-ledger-the-rising-profile-of-financial-planning-analysis/.
Wladawsky-Berger, Irving. “As Big Data and AI Take Hold, What Will It Take to Be an Effective Executive?” Wall Street Journal, January 23, 2015. Accessed February 1, 2016. https://blogs.wsj.com/cio/2015/01/23/as-big-data-and-ai-take-hold-what-will-it-take-to-be-an-effective-executive/.
Zuckerman, Gregory and Bradley Hope. “The Quants Run Wall Street Now,” Wall Street Journal. May 21, 2017. Accessed June 1, 2017. https://www.wsj.com/articles/the-quants-run-wall-street-now-1495389108.

Foundations of Computational Finance with MATLAB®