An Undergraduate Introduction to Financial Mathematics

Overview

This textbook provides an introduction to financial mathematics and financial engineering for undergraduate students who have completed a three- or four-semester sequence of calculus courses. It introduces the theory of interest, discrete and continuous random variables and probability, stochastic processes, linear programming, the Fundamental Theorem of Finance, option pricing, hedging, and portfolio optimization. This third edition expands on the second by including a new chapter on the extensions of the ...

See more details below
Other sellers (Hardcover)
  • All (10) from $58.71   
  • New (7) from $58.71   
  • Used (3) from $59.11   
An Undergraduate Introduction to Financial Mathematics

Available on NOOK devices and apps  
  • NOOK Devices
  • Samsung Galaxy Tab 4 NOOK
  • NOOK HD/HD+ Tablet
  • NOOK
  • NOOK Color
  • NOOK Tablet
  • Tablet/Phone
  • NOOK for Windows 8 Tablet
  • NOOK for iOS
  • NOOK for Android
  • NOOK Kids for iPad
  • PC/Mac
  • NOOK for Windows 8
  • NOOK for PC
  • NOOK for Mac
  • NOOK for Web

Want a NOOK? Explore Now

NOOK Book (eBook)
$56.00
BN.com price

Overview

This textbook provides an introduction to financial mathematics and financial engineering for undergraduate students who have completed a three- or four-semester sequence of calculus courses. It introduces the theory of interest, discrete and continuous random variables and probability, stochastic processes, linear programming, the Fundamental Theorem of Finance, option pricing, hedging, and portfolio optimization. This third edition expands on the second by including a new chapter on the extensions of the Black-Scholes model of option pricing and a greater number of exercises at the end of the each chapter. More background material has been added to the other chapters, allowing the textbook to better stand alone as an introduction to financial mathematics. The reader progresses from a solid grounding in multivariable calculus through a derivation of the Black-Scholes equation, its solution, properties, and applications. The text attempts to be as self-contained as possible without relying on advanced mathematical and statistical topics. The material presented in this book will adequately prepare the reader for graduate-level study in mathematical finance.

Read More Show Less

Product Details

  • ISBN-13: 9789814407441
  • Publisher: World Scientific Publishing Company, Incorporated
  • Publication date: 7/28/2012
  • Edition number: 3
  • Pages: 464
  • Sales rank: 1,263,965
  • Product dimensions: 6.00 (w) x 8.90 (h) x 1.20 (d)

Table of Contents

Preface vii

Preface to the Second Editions ix

Preface to the First Edition xi

1 The Theory of Interest 1

1.1 Simple Interest 1

1.2 Compound Interest 3

1.3 Continuously Compounded Interest 4

1.4 Present Value 6

1.5 Time-Varying Interest Rates 12

1.6 Rate of Return 14

1.7 Continuous Income Streams 15

1.8 Exercises 17

2 Discrete Probability 21

2.1 Events and Probabilities 22

2.2 Addition Rule 23

2.3 Conditional Probability and Multiplication Rule 24

2.4 Random Variables and Probability Distributions 27

2.5 Binomial Random Variables 28

2.6 Expected Value 30

2.7 Variance and Standard Deviation 38

2.8 Exercises 42

3 Normal Random Variables and Probability 47

3.1 Continuous Random Variables 47

3.2 Expected Value of Continuous Random Variables 50

3.3 Variance and Standard Deviation 54

3.4 Normal Random Variables 55

3.5 Central Limit Theorem 64

3.6 Lognormal Random Variables 66

3.7 Properties of Expected Value 70

3.8 Properties of Variance 73

3.9 Exercises 76

4 The Arbitrage Theorem 81

4.1 The Concept of Arbitrage 83

4.2 An Introduction to Linear Programming 84

4.3 Dual Problems 91

4.4 The Fundamental Theorem of Finance 103

4.5 Exercises 106

5 Random Walks and Brownian Motion 111

5.1 Intuitive Idea of a Random Walk 111

5.2 Discrete Random Walks 112

5.3 First Step Analysis 116

5.4 Continuous Random Walks 127

5.5 The Stochastic Integral 134

5.6 Continuous Random Walks with Drift 137

5.7 Itô Processes 143

5.8 Itô's Lemma 144

5.9 Stock Market Example 148

5.10 Exercises 150

6 Forwards and Futures 155

6.1 Definition of a Forward Contract 155

6.2 Pricing a Forward Contract 157

6.3 Dividends and Pricing 162

6.4 Incorporating Transaction Costs 163

6.5 Futures 165

6.6 Exercises 168

7 Options 173

7.1 Properties of Options 174

7.2 Including the Effects of Dividends 178

7.3 Pricing an Option Using a Binary Model 180

7.4 Black-Scholes Partial Differential Equation 182

7.5 Boundary and Initial Conditions 184

7.6 Option Strategies 186

7.7 Exercises 194

8 Solution of the Black-Scholes Equation 199

8.1 Fourier Transforms 199

8.2 Inverse Fourier Transforms 202

8.3 Changing Variables in the Black-Scholes PDE 203

8.4 Solving the Black-Scholes Equation 207

8.5 Binomial Model (Optional) 211

8.6 Exercises 223

9 Derivatives of Black-Scholes Option Prices 227

9.1 Theta 227

9.2 Delta 229

9.3 Gamma 231

9.4 Vega 232

9.5 Rho 233

9.6 Relationships Between Δ, Θ, and Γ 235

9.7 Exercises 237

10 Hedging 241

10.1 General Principles 241

10.2 Delta Hedging 244

10.3 Delta Neutral Portfolios 249

10.4 Gamma Neutral Portfolios 250

10.5 Exercises 252

11 Extensions of the Black-Scholes Model 255

11.1 Options on Stocks Paying Continuous Dividends 255

11.2 Options on Stocks Paying Discrete Dividends 260

11.3 Exercises 267

12 Optimizing Portfolios 271

12.1 Covariance and Correlation 271

12.2 Optimal Portfolios 279

12.3 Utility Functions 282

12.4 Expected Utility 288

12.5 Portfolio Selection 290

12.6 Minimum Variance Analysis 294

12.7 Mean-Variance Analysis 305

12.8 Exercises 310

13 American Options 315

13.1 Parity and American Options 315

13.2 American Puts Valued by a Binomial Model 321

13.3 Properties of the Binomial Pricing Formula 328

13.4 Optimal Exercise Time 331

13.5 Exercises 336

Appendix A Sample Stock Market Data 339

Appendix B Solutions to Chapter Exercises 343

B.1 The Theory of Interest 343

B.2 Discrete Probability 349

B.3 Normal Random Variables and Probability 359

B.4 The Arbitrage Theorem 373

B.5 Random Walks and Brownian Motion 381

B.6 Forwards and Futures 394

B.7 Options 399

B.8 Solution of the Black-Scholes Equation 407

B.9 Derivatives of Black-Scholes Option Prices 416

B.10 Hedging 421

B.11 Extensions of the Black-Scholes Model 430

B.12 Optimizing Portfolios 434

B.13 American Options 445

Bibliography 455

Index 459

Read More Show Less

Customer Reviews

Be the first to write a review
( 0 )
Rating Distribution

5 Star

(0)

4 Star

(0)

3 Star

(0)

2 Star

(0)

1 Star

(0)

Your Rating:

Your Name: Create a Pen Name or

Barnes & Noble.com Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & Noble.com that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & Noble.com does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at BN.com or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation

Reminder:

  • - By submitting a review, you grant to Barnes & Noble.com and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Noble.com Terms of Use.
  • - Barnes & Noble.com reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & Noble.com also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on BN.com. It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

 
Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously

    If you find inappropriate content, please report it to Barnes & Noble
    Why is this product inappropriate?
    Comments (optional)