NYU Stern School of Business

Undergraduate College


Fall 2012

Instructor Details

Lakner, Peter


1 212 998-0476


KMEC 8-61


Course Meetings

T, 6:00pm to 9:00pm

Tisch T-200

Final Exam:

Schedule exceptions
    Class will not meet on:
    Class will meet on:


Course Description and Learning Goals

The class will cover the basic concepts of Financial Engineering, emphasizing the computational aspects of the subject. Topics will include martingale measures, arbitrage, the general pricing formula, put and call options, the binomial model, pricing European call options in the binomial and in the Black-Scholes model, American and exotic options, forward and futures contracts.  The objective of the class is that students acquire a hand-on experience in the computations related to the above concepts.


Course Pre-Requisites

An introductory course in Statistics, knowledge of binomial and normal distributions, use of the normal probability table, expected value and standard deviation of a distribution, conditional probabilities. Solving a system of linear equations. Calculus is NOT necessary for this class.



Course Outline

10/2 Stock prices, trading strategies, value process, gains, discounting, arbitrage, risk-neutral probability measures, the fundamental theorem of asset pricing.

10/9 Pricing attainable contingent claims, Call and put options, complete and incomplete markets.

10/16 Pricing non-attainable contingent claims, the put-call parity, multiperiod markets, event algebras.

10/23 Trading strategy, gains and wealth processes in a multiperiod setting, discounting, conditional expectation with respect to an event algebra, martingales, arbitrage, martingale measure. The fundamental theorem of asset pricing in a multiperiod setting.

10/30 Martingale measure for a market with dividend paying stocks, contingent claims, arbitrage pricing in a multiperiod setting, put-call parity and the chooser option.


11/13 The binomial model, the European call option under the binomial model.

11/20 Lookback, knockout and Asian options. American options.

11/27 The Bermudan option, forward contracts on stocks without and with dividends.

12/4 Futures. The Black-Scholes model, the BS formula, hedging the European call in the BS model.

12/11 Sensitivity analysis of the Black-Scholes formula, Approximation of the Black-Scholes formula with the binomial option-pricing formula. Zero-coupon bonds, the yield curve.



Required Course Materials

Pliska, S.R., Introduction to Mathematical Finance. This book is available in the NYU Bookstore.


Assessment Components

The grade will be based on the two exams and the homework assignments. The weights are 40% for each exam and 20% for the homework assignments.



Group Projects

There will be no group projects, all homework assignments will be required to contain only individual work.



At NYU Stern we seek to teach challenging courses that allow students to demonstrate their mastery of the subject matter. Assigning grades that reward excellence and reflect differences in performance is important to ensuring the integrity of our curriculum.

In general, students in this elective course can expect a grading distribution where about 50% of students will receive A’s for excellent work and the remainder will receive B’s for good or very good work. In the event that a student performs only adequately or below, he or she can expect to receive a C or lower.

Note that the actual distribution for this course and your own grade will depend upon how well each of you actually performs in this course.



The process of assigning grades is intended to be one of unbiased evaluation. Students are encouraged to respect the integrity and authority of the professor’s grading system and are discouraged from pursuing arbitrary challenges to it.

If you believe an inadvertent error has been made in the grading of an individual assignment or in assessing an overall course grade, a request to have the grade re-evaluated may be submitted. You must submit such requests in writing to me within 7 days of receiving the grade, including a brief written statement of why you believe that an error in grading has been made.


Professional Responsibilities For This Course




In-class contribution is a significant part of your grade and an important part of our shared learning experience. Your active participation helps me to evaluate your overall performance.
You can excel in this area if you come to class on time and contribute to the course by:




Classroom Norms


Academic Integrity

Integrity is critical to the learning process and to all that we do here at NYU Stern. As members of our community, all students agree to abide by the NYU Stern Student Code of Conduct, which includes a commitment to:

The entire Stern Student Code of Conduct applies to all students enrolled in Stern courses and can be found here:

Undergraduate College: http://www.stern.nyu.edu/uc/codeofconduct
Graduate Programs: http://w4.stern.nyu.edu/studentactivities/involved.cfm?doc_id=102505

To help ensure the integrity of our learning community, prose assignments you submit to Blackboard will be submitted to Turnitin.  Turnitin will compare your submission to a database of prior submissions to Turnitin, current and archived Web pages, periodicals, journals, and publications.  Additionally, your document will become part of the Turnitin database.


Recording of Classes

Your class may be recorded for educational purposes


Students with Disabilities

If you have a qualified disability and will require academic accommodation of any kind during this course, you must notify me at the beginning of the course and provide a letter from the Moses Center for Students with Disabilities (CSD, 998-4980, www.nyu.edu/csd) verifying your registration and outlining the accommodations they recommend.  If you will need to take an exam at the CSD, you must submit a completed Exam Accommodations Form to them at least one week prior to the scheduled exam time to be guaranteed accommodation.


Stern Policies

General Behavior
The School expects that students will conduct themselves with respect and professionalism toward faculty, students, and others present in class and will follow the rules laid down by the instructor for classroom behavior.  Students who fail to do so may be asked to leave the classroom. 


Collaboration on Graded Assignments
Students may not work together on graded assignment unless the instructor gives express permission. 


Course Evaluations
Course evaluations are important to us and to students who come after you.  Please complete them thoughtfully.


Printer Friendly Version