NYU SHANGHAI
Business Division
Derivatives
BUSF-SHU 48
Fall 2025
Professors
Online:
Tutorial:
Marti G. Subrahmanyam
Johnson Mo
Tu 07:00 pm - 09:30 pm (CST)
Th 06:15pm - 07:30 pm (CST)
Course Description:
This course consists of three sections. The first section deals with the institutional setting, and
concepts including pricing and hedging of forward and futures markets. The second section covers the
institutional setting, and concepts including pricing and hedging of options markets, broadly defined. The
third section is designed to provide a broad exposure to the subject of interest rate derivative products, both
swaps and options. The course will conclude with a brief introduction to exotic derivative product. The
emphasis of the course will be on hedging, trading, portfolio and risk management applications of derivatives
products and markets.
In the first section of the course, the basic concepts of derivatives, including arbitrage and hedging,
will be introduced and applied to the pricing of futures and forward contracts on commodities, stock indices,
foreign exchange, and fixed income securities. The discussion will be in the context of the setting of financial
markets, institutions, and products
The second section will include a detailed discussion of option pricing, hedging, and trading strategies
in the context of the management of the risk of a derivatives book, based mainly on the principles of arbitrage
underlying the Black-Scholes-Merton model and its variants. Although the principles developed in this
course are relevant to the pricing and hedging of any derivative asset, their applications to the specific cases
of options on stocks, stock indices, foreign exchange, futures contracts and interest rate instruments are
analyzed.
The topics covered in the third part of the course include the relationship of swaps to other fixed
income contracts such as futures contracts and forward rate agreements, valuation and hedging of swaps, and
interest rate options, with particular reference to caps, floors and swaptions. The application of these
concepts to foreign exchange and commodity derivatives is also discussed in this section. Depending on the
time available, there will be a brief introduction to exotic options.
The pedagogy in this half of the course is a combination of lectures/discussions and PC-based
problem solutions. The course is intensive and requires a fair amount (~ 6-8 hours) of homework each week,
in addition to preparation for class. The orientation of the course is the practical application of derivatives
concepts, rather than a discussion of derivatives pricing theory by itself. However, since option concepts are
somewhat mathematical, a strong quantitative background, though not required, would be an advantage.
Required Material:
You are responsible for the material covered in class and posted on Brightspace. Readings and other
class materials will also be posted. The problem sets and all e-mail communications are part of the class
materials.
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Required/Recommended Textbooks/Software:
Recommended: J.C. Hull, Fundamental of Futures and Options, 9th edition, Prentice-Hall, 2017. (H)
Optional: R. Sundaram and S. Das, Derivatives: Principles and Practice, 2nd edition, McGraw Hill/Irwin,
2013.
The book by Hull is probably the most comprehensive undergraduate derivatives textbook available
today. We will use it as background, but will not follow it closely. The relevant chapters from the book are
listed in the course outline, market “H.” The book by Sundaram and Das is more intuitive, and has a more
detailed discussion of credit derivatives. There are several software packages available for pricing and
hedging of derivatives. Of these, FINCAD© is a widely used package that has pricing and hedging models
for a wide range of derivatives instruments with Excel add-ins. It has a free demo version that can be used
for a limited period of time.
Other Materials:
--
Copies of overhead transparencies: Books I to V. [To be handed out in class. Also, available on the
course website on Brightspace.]
--
Problem sets and computer exercises. [To be handed out in class. Also, available on the course
website on Brightspace.]
--
Option pricing/hedging software. [Available on the course website on Brightspace.]
Market Tracking:
You are expected to follow financial markets on a regular basis. In particular, you should pay attention
to the fair value of Gold futures, SPX futures, and the implied volatility of index options (e.g., VIX). Market
tracking questions may appear on the exams.
You should regularly check internet websites related to derivatives including those of major exchanges,
such as the CME, CBOE, and Bloomberg. You are also expected to read the financial press, with special
attention to the futures and options columns in the Wall Street Journal, and the Financial Times.
Instructions:
Students in the course are expected to study the readings and problem sets prior to the assigned dates
and come prepared to discuss them in class. The following outline represents the topics, readings,
assignments and dates for discussion. The reference dates noted are rough estimates for the time allotted to
each subject area. Any modifications of the schedule will be announced in class.
There are three problem sets in the second section of the course – roughly one every other week
throughout the course. There may also be a fourth problem set, which would be optional In many instances,
students are required to use PC-based software for the solution of the problem sets. Solutions to the problem
sets should be worked out, printed and handed in prior to class on the dates they are due. Hand calculators
will be necessary for problem sets and examinations. The lectures and reading materials assigned will, in
many instances, provide an appropriate format for analysis and solution of the problem sets.
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Class Attendance:
Students are required to attend all classes and be on time. Given the potential delays in admitting
students to class Zoom sessions, it would be best to join the online sessions five minutes prior to the beginning
of class. Based on past experience, much of the learning in the course is from participating in the class
discussions. Absence from class will affect the final grade.
All class sessions will be videotaped and webcast. However, viewing these recordings is meant to
be a supplement and not a substitute for attending class sessions.
Classroom Etiquette, Stern Honor Code, and Related Matters:
Students who come in late should enter the Zoom as quietly as possible. Since class participation is
assessed and forms part of the grade in the course, regular class attendance is required. In line with school
policy, the use of laptop computers, cellular phones and mobile communication devices, and other electronic
equipment for purposes other than following the class discussion is not allowed during class sessions.
Our undergraduate Academics Pillar states that we take pride in our well-rounded education and
approach our academics with honesty and integrity. Indeed, integrity is critical 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:
•
Exercise integrity in all aspects of one's academic work including, but not limited to, the preparation
and completion of exams, papers and all other course requirements by not engaging in any method
or means that provides an unfair advantage.
•
Clearly acknowledge the work and efforts of others when submitting written work as one’s own.
Ideas, data, direct quotations (which should be designated with quotation marks), paraphrasing,
creative expression, or any other incorporation of the work of others should be fully referenced.
•
Refrain from behaving in ways that knowingly support, assist, or in any way attempt to enable another
person to engage in any violation of the Code of Conduct. Our support also includes reporting any
observed violations of this Code of Conduct or other School and University policies that are deemed
to adversely affect the NYU Stern community.
•
Students should adhere to the Stern Honor Code and every student is obligated to report to the
instructor any suspected violation of the code that he or she has observed. Further instructions are
available at http://www.stern.nyu.edu/UC/CurrentStudents/CodeofConduct/index.htm
To help ensure the integrity of our learning community, prose assignments you submit to Brightspace
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.
If you 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 Student Accessibility (212-9984980, mosescsa@nyu.edu) verifying your registration and outlining the accommodations they recommend.
If you will need to take an exam at the Moses Center for Student Accessibility, you must submit a completed
Exam Accommodations Form to them at least one week prior to the scheduled exam time to be guaranteed
accommodation. For more information, visit the CSA website: https://www.nyu.edu/students/communitiesand-groups/student-accessibility.html
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Name Pronunciation and Pronouns:
NYU Stern students now have the ability to include their pronouns and name pronunciation in Albert.
I encourage you to share your name pronunciation and preferred pronouns this way. Please utilize this link
for additional information: Pronouns & Name Pronunciation
Religious Observances and other unique situations:
NYU Stern is committed to ensuring an equitable educational experience for all students regardless
of identity or religious/cultural background. The observance of religious and cultural holidays/traditions and
the recognition of unique circumstances - such as serving as a caregiver -are important aspects of this
commitment. Except for religious observances or other absences that may be required in compliance with
nondiscrimination law, this class otherwise requires attendance and participation and cannot accommodate
conflicts. Please review all class dates at the start of the semester and review all course requirements to
identify any foreseeable conflicts with exams, course assignments, projects, or other items required for
participation and attendance. If the observance of religious and cultural holidays/traditions and/or the
recognition of unique circumstances - such as serving as a caregiver will prevent you from attending class,
please be aware that this particular course requires 100% attendance. Please review all class dates to ensure
you can attend all of them. If you identify any foreseeable conflicts with class attendance, exams, or other
items required for participation and attendance, it is strongly recommended that you do not take this class.
This course strives to support and cultivate diversity of thought, perspectives, and experiences. The intent is
to present materials and activities that will challenge your current perspectives with a goal of understanding
how others might see situations differently. By participating in this course, it is the expectation that everyone
commits to making this an inclusive learning environment for all.
Zoom Instructions:
The online mode of instruction that we are all getting familiar with poses a number of challenges. To make
this experience more efficient and pleasant for all of us, I recommend that we all follow some basic rules:
-
Label your names correctly and completely with your first and last names, and not “Joe’s Laptop” or
“Hock-Hwa’s Ipad.”
Come to the Zoom room at least five minutes before class, i.e., before 10.55 am each
Tuesday/Thursday.
Please mute yourself upon entering the Zoom room
Please stay muted unless you wish to speak. Do not switch off your video feed.
Put your hand up on Zoom if you wish say something
When we go into breakout rooms, please exit the main room and join your breakout rooms without
delay. Re-enter the main room at the end of assigned time.
Learn to answer the polls when they are announced.
Course Prerequisites:
All core courses.
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Office Hours:
Professor Subrahmanyam:
Mondays:
10:50 am-12:20 pm (NY Time)
Tuesdays:
09:30 am-10:30 pm (NY Time)
September 1 – December 14, 2025.
and by appointment. (Please email Michael Pierre-Jules at mj37@stern.nyu.edufor an appointment.)
Office:
KMC #9-69
Zoom: https://nyu.zoom.us/my/martisubrahmanyam
e-mail: msubrahm@stern.nyu.edu
Professor Mo:
Wednesdays: 3:30 pm – 4:30 pm (CST)
Office:
NYU Shanghai S806
e-mail: jm3499@nyu.edu
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COURSE OUTLINE
Date
Sess. No.
9/2 T
I
9/2 T
9/9 T
9/9 T
9/12 F
II
III
IV
V
Subject
Introduction to Derivatives Markets
•
Definitions of Derivative Contracts: Linear vs. Non-linear Contracts
•
Forwards, Futures, and Swaps
•
Call and Put Options
•
History of Derivatives Contracts
The Structure of Derivatives Contracts
•
Over-the-counter vs. Exchanged Traded Contracts
•
Trading, Clearing and Delivery
Arbitrage and the Cost of Carry Model
•
Commodities e.g., Gold, Oil, Wheat etc.
•
Stock Indices
Arbitrage and the Cost of Carry Model
•
Foreign Exchange
•
Interest Rates e.g., Libor (Eurodollar) and Fed Funds
Arbitrage and the Cost of Carry Model
•
9/12 F
9/29 T
VI
Chapter or Source
Treasury Notes and Bonds
Hedging with Futures Contracts
•
Statistical Arbitrage
•
PVBP and Duration Hedging
•
Problems with Hedging:
▪
Metallgesselschaft?
▪
LTCM
▪
Ashanti Gold Mines
National Holiday Break
Problem Set # 1 (due 9.29)
Forwards and Futures Pricing
6
10/7 T
10/7 T
VII
VIII
Option Definitions and Payoffs
•
Definition of the Contracts
•
Payoff Diagrams
•
Basic Option Trading Strategies
•
Reverse Engineering of Option Payoffs
Arbitrage-Based Pricing Restrictions
•
No-arbitrage Restrictions
H, Ch. 11 (to p. 241)
•
Early Exercise of American Options
H, Ch. 11 (pp. 244-250)
Problem Sets # 2 (due 10/9)
Option Payoff Diagrams
10/10 F
10/10 F
IX
X
Static Arbitrage Relationships
•
Put-Call Parity: European
•
Dividends and Early Exercise
•
Put-Call Parity: American
The Binomial Model
•
Single-stage Model
•
Riskless Hedge
•
Replication
Problem Sets # 3 (due 10/17)
Arbitrage Restrictions
10/14 T
10/14 T
XI
XII
The Binomial Model (Contd.)
•
Risk-Neutral Probability
•
Multiple Stages
The Binomial Model (Contd.)
•
American Options
•
Dynamic Hedging
Problem Sets # 4 (due 10/24)
Put-Call Parity
7
10/21 T
XIII
The Two-Period Binomial Model
10/21 T
XIV
The n-Period Binomial Model
•
Construction of Binomial Lattices
•
The Limiting Case
The Black-Scholes-Merton Model
10/30 Tu
•
Interpretation of Volatility
•
Simple Proof of the Model
H, Ch. 21 (pp. 280-292)
H, Ch.11 (pp. 307-317)
Room: TBA
In-Class Midterm during Recitation
10/28 T
10/28 T
XV
XVI
The Black-Scholes-Merton Model (Contd.)
•
Alternative Proofs (Intuition)
•
Computational Issues
•
Extensions: Futures (Black)
•
Stock Indices, Dividends, Foreign Exchange H, Ch.15, Ch.16
H, Ch. 21 (pp. 291-292)
H, Ch.13
The Black-Scholes-Merton Model (Contd.)
•
Alternative Assumptions
•
Hedge Ratio
H, Ch.19
•
Implied Volatility
M. Brenner/M. Subrahmanyam
Problem Set # 5 (due 11/17)
Binomial Model
11/4 T
XVII
The Black-Scholes Model (Contd.)
•
Measurement of Volatility
•
Empirical patterns of volatility:
smile, mean-reversion
11/4 T
11/11 T
XVIII
XIX
H, Ch. 13
Sensitivity Analysis I (Option Values)
•
Option Delta
•
Option Theta, Vega (Kappa)
H, Ch.17 (to p. 370)
Sensitivity Analysis II (Option Hedge Ratios)
8
11/11 T
XX
•
Option Gamma
H, Ch.18 (after p. 371)
•
Option Omega
Brenner/Subrahmanyam (2)
Option Position Analyses
•
Position Delta
•
Position Gamma
•
Position Theta
•
Position Vega
Problem Set # 6 (due 11/24)
Option Prices and Hedge Ratios
11/18 T
XXI
Value at Risk
H, Ch. 20
•
Basic Concepts
•
Measurement Issues
•
BIS Requirements
Futures and Forward Contracts
11/18 T
XXII
•
Definitions and Basics of Pricing
•
Over-the-Counter and Exchange-Traded Products
•
Forward Rate Agreements
Basics of Interest Rate Swaps and FRAs
•
Relationship between FRAs and Swaps
•
Relationship between Swaps and Bonds
•
Spot - Forward Parity, Pricing of FRAs
•
Convexity Differences between FRAs and Futures
•
Adjusting for Convexity
H, Ch. 1, Ch. 2 (skim)
H, Ch. 7
Problem Set # 7 (due 12/01)
Options Hedging Strategies
11/25 T
XXIII
Pricing, Valuation and Hedging of Swaps
•
Valuation of Interest Rate Swaps: Principal and
•
Forward Methods
•
PVBP Analysis and Hedging of a Swap Portfolio
•
Other Swaps: Currency, Equity, Commodity etc.
H, Ch. 7
9
H, Ch. 33
11/25 T
XXIV
Interest Rate Option Pricing/Hedging
H, Ch. 29 (to p. 684)
•
European Options on Bonds and Interest Rates
•
Option Payoffs and Strategies for Interest Rate Options
•
Classification of Interest Rate Options Products
•
Interest Rate Caps and Floors
•
Interest Rate Swaptions
H, Ch. 29 (after p. 684)
Problem Set # 8 (due 12/08)
FRA’s and Swaps
12/2 T
12/9 T
XXV
Exotic Options
H, Ch. 26
•
Features of exotics
•
Main types
•
Binomial model of valuation/hedging
•
Uses of exotic options
•
Path-dependent options: Knock-out/Knock-in options
•
Path-dependent options: Asian options
•
Other exotic options
XXVI
Review Session
TBD
XXVII
Final Exam
10