MATH M451 The Mathematics of Finance
MATH M551 Markets and Multi-Period Asset Pricing
INFO I400/I590 Foundations of Financial Engineering
Fall 2016

Esfandiar Haghverdi
Informatics East 216
Office Hours: By appointment only.


Monday, Wednesday
02:30 pm - 03:45 pm, SE 140



Weekly schedule

Course Description According to John C. Hull the author of the famous textbook Options, Futures, and Other Derivatives, "In the last 30 years, derivatives have become increasingly important in finance. Futures and options are actively traded on many exchanges throughout the world. Many different types of forward contracts, swaps, options, and other derivatives are entered into by financial institutions, fund managers, and corporate treasurers in the over-the- counter market. Derivatives are added to bond issues, used in executive compensation plans, embedded in capital investment opportunities, used to transfer risks in mortgages from the original lenders to investors, and so on. We have now reached the stage where those who work in finance, and many who work outside finance, need to understand how derivatives work, how they are used, and how they are priced. Whether you love derivatives or hate them, you cannot ignore them!"

In this course, we will explore the mathematics behind Black-Scholes-Merton (BSM) option pricing theory and will derive the BSM formula. The approach will be mathematically rigorous at the appropriate level to senior undergraduate and beginning graduate students. BSM theory was published in 1973 by Fischer Black and Myron Scholes in their paper, "The Pricing of Options and Corporate Liabilities", published in the Journal of Political Economy. Robert C. Merton published a paper, "Theory of Rational Option Pricing" in Bell Journal of Economics and Management Science expanding the mathematical understanding of the options pricing model, also in 1973. Merton and Scholes received the 1997 Nobel Memorial Prize in Economic Sciences for their work. Black died in 1995 and was therefore not eligible for the prize. BSM is one of the most beautiful and useful results in mathematical finance.

P: MATH M311 and MATH M365 or equivalent.

Learning Outcomes:

  • The ability to understand the notion of a financial derivative.
  • The ability to appreciate the importance of financial derivatives in today's financial markets.
  • The ability to reason about the structure and payoff of a derivative.
  • The ability to price an option using Balck-Scholes-Merton formula.
  • The ability to explain the mechanics of the derivation of the Black-Scholes-Merton formula.
  • The ability to understand the foundational mathematics required for financial modeling.
  • The ability to design simple financial contracts.

Topics covered:

  • Introduction to futures, forwards, and options
  • Stock options and their purpose
  • An aperitif on arbitrage
  • Discrete probability
  • Stochastic processes, filtrations and martingales
  • Discrete-Time pricing models
  • The Binomial Model
  • Pricing nonattainable alternatives in an incomplete market
  • Optimal stopping and American Options
  • Continuous probability
  • The BlackÔÇôScholes option pricing formula

Required Textbook:

  • Introduction to the Mathematics of Finance. Steven Roman, second edition. Undergraduate Texts in Mathematics, Springer-Verlag, 2012.
    Available electronically through IUCAT

Recommended Textbooks:

  1. Options, Futures, and Other Derivatives.John C. Hull, 8th Edition. Prentice Hall, 2012.

Optional reading list:

  1. Capital Ideas: The Improbable Origins of Modern Wall Street. Peter L. Bernstein. The Free Press, 1992.
  2. When Genius Failed. Roger Lowenstein. Random House Trade Paperbacks, 2011.

Interesting/useful sites:

  1. Bank for International Settlements
  2. CME Group
  3. CBOE
  4. NYSE
  6. Japan Exchange Group
  7. SSE
  8. NSE
  9. Investopedia
  10. Trading Technologies

Handouts and Homework: All handouts and homework assignments will be posted on Canvas.

Associate Instructor (Grader):

Hemant Pandey.


  • Weekly Quiz: 15%
  • Homework assignments: 15%
    • There will be weekly homework.
    • Each homework will consist of the following parts:
      1. Regular problems: A set of problems chosen from several sources including the textbooks above.
      2. Reading assignment from the textbook or other handouts.
    • Each homework will be assigned on a Wednesday and will be due the Wednesday after, in class.
    • Solutions must be written LEGIBLY.
    • It is encouraged to discuss the problem sets with others, but everyone needs to turn in a unique personal write-up.
  • Midterm I: 20%
    • Midterm I is scheduled on September 28, 2016 in class.
  • Midterm II: 20%
    • Midterm II is scheduled on November 7, 2016 in class.
  • Final exam: 30%.
    • Final exam will be on 2:45-4:45 p.m., Mon., December 12

Ground rules:

  • I strongly advise you to attend all the classes and take good notes.
  • Late homework will NOT be accepted. However, the lowest homework grade will be dropped.
  • There will be NO make-up midterm exams.
  • The final grade will be calculated according to the evaluation scheme given above and these grades will then be curved to determine your letter grades. However if you get less that 25/100 on the final exam or your total grade is less than 45/100 your final grade will automatically be an F.
  • NO Incomplete grades will be given under any condition.
  • NO extra work, extra credit or anything outside the regular homeworks and midterms will be assigned. Please plan your study strategy during the term accordingly.
  • Grading mistakes:
    If during the semester you feel there has been a mistake made in your grading by the AIs, please contact them first. If after meeting with the AIs you still feel there is a problem with the marking, please contact me.
  • Collaborative work:
    One of the best ways to learn new material is to collaborate in groups. You may discuss the homework problems with your classmates, and in this way make the learning process more enjoyable. However, the homework you hand in must be your own work, in your own words and your own explanation.
  • Here is the link to The Code of Student Conduct.