Microsoft Word - March 2021 Pre-module Assignment.doc
PRE-MODULE ASSIGNMENT
Module 2A: Derivatives Markets
Prof Menachem Brenner
March 07 – 09, 2021 (Sun - Tue)
Message from Prof. Menachem Brenner:
* Futures: Q3 is an open exercise that does not have a pre-set answer.
* Options: Q1 is an open exercise that does not have a pre-set answer.
You will be mainly evaluated on the non-open questions.
Module 3:
Pre-module Assignment 20%
In-class Assignments/Participation 20%
Final Take-home Exam 60%
Deadline: XXXXXXXXXXhours (NY Time), March 06, 2021 (Saturday) /
1259 hours (HK Time), March 07, 2021 (Sunday)
Enquiry:
If you have any question, please contact our Teaching Assistant Hae Kang Lee at
XXXXXXXXXX
Assignment Submission:
- Please submit your assignment on Canvas by the deadline. No submissions will be accepted by
email. Please ensure that your name appears on all attachments.
- Please submit your assignment in PDF format.
Important Note
Concepts related to problem sets in this assignment will be discussed during the tutorial of Module 2A.
Late submission will not be accepted and will result in zero mark.
MS in Global Finance Module 2A: Derivatives Markets
Prof Menachem Brenner | Pre-module Assignment
2 of 3
This pre-module assignment focuses on the basics of futures and options. The futures questions deal
with ‘fair’ valuation of futures contracts and how the information from market prices can be used. The first
two problems deal with gold futures and foreign exchange futures. The third one deals with index
a
itrage. The options questions deal with payoff (profit) diagrams and basic strategies.
Though you could answer these problems without knowing the detailed specification of the contracts, in
eality when you trade in these markets you must familiarize yourself with the market’s operations and
contract specifications.
Futures:
Q1. Suppose the spot price of gold is $1880 per ounce. The futures price for delivery in six months is
$1891, while the futures price for delivery in one year is $1902. The interest rate on 6-month
loans is 1.00 percent (on an annual basis, continuous compounding).
a. Ignoring transactions costs, does this represent an a
itrage opportunity? Why?
. What is the implied interest rate for the first six months?
c. What is the implied forward rate six months hence? (Recall computing forward rates from
onds with different maturities). Is the yield curve upward sloping?
d. Suppose the spot price of gold is, instead, $1883 per ounce and the six months futures has
not changed XXXXXXXXXXAssuming gold can be sold short at a transactions cost of $2.0 per
ounce (paid up front), describe an a
itrage strategy. What are the a
itrage gains, if any?
Q2. Suppose the spot price for Euro is $1.25, the futures price for delivery in 6 months is $1.255.
Assume that the 6 month bo
owing/lending rate in Euro is 0.25 percent (annually, continuous
compounding) and the co
esponding rate in $ is 0.75 percent (annually, continuous
compounding). (This is an FX application using the same cost of ca
y model).
a. Assume no transactions costs, do the above prices represent an a
itrage opportunity?
Why?
. What are the implied interest rates in Europe and the U.S.?
Q3. Compute the ‘fair’ value of the next two futures contracts (March & June 2021) on the S&P500
Index (SPX) using SPX as the underlying asset (this is an open question, no one specific solution
since it depends on the day/time that each of you is using and the rates that you think are
elevant).
Answer the following questions:
a. What interest rate and dividend yield did you use?
. Did the futures contract settle above or below SPX?
c. What are the transaction costs in index a
itrage activity?
d. What are the implied interest rates using the settlement prices?
e. What are the issues in doing index a
itrage (e.g. short selling)?
MS in Global Finance Module 2A: Derivatives Markets
Prof Menachem Brenner | Pre-module Assignment
3 of 3
Options:
Q1. The first simple exercise that you should try is to draw payoff diagrams (or profit diagrams) of
various strategies. Get the web page http:
www.cboe.com/DelayedQuote/QuoteTable.aspx for the
closing prices of SPY options, or use the quotes on Bloomberg or Yahoo Finance. (Notice; payoffs
do not include the option premium (price) while profits include the option premium (price)).
Here are a few possible strategies: (additional examples will be presented and discussed in class).
a. Buy the near term ATM (at-the-money) straddle.
. Write the near term ATM call spread.
c. Buy the near term ATM put spread.
d. Write the near term ATM butterfly spread.
e. Buy 1 basket (SPX or HSI), Buy 1 near term ATM put
f. Buy 1 near term ATM put; Write 1 near term ATM call
g. Buy an ATM put spread; Buy an ATM call spread
Q2. In each of the following 5 cases, what strategy will assure a profit if options on gold are priced as
XXXXXXXXXXfollows:
a. C(K = 1900, T1 = Apr.) > C(K = 1900, T2 = June)
b. C(K = 1920, T1 = Apr.) > C(K = 1900, T1 = Apr.)
c. C(K = 1900, T1 = Apr.) > C(K = 1920, T2 = June)
d. C(K = 1900, T1 = Apr.) < (S - PV(K))
e. P(K = 1900, T1 = Apr.) > C(K = 1900, T1 = Apr.)
Q3. The following three call options on gold, all expiring in three months, sell for:
Exercise price Option price
$1850 $ 120
$1900 $ 90
$1950 $ 70
Consider the following position:
buy 1 call with K = 1850
sell (write) 2 calls with K = 1900
buy 1 call with K = 1950
What would be the values at expiration of such a spread for various prices of spot gold? What
investment would be required to establish the spread? Given information about the prices of the
$1850 and $1950 options, what could you predict about the price of the $1900 option?
Professor Gan’s Comments:
PRE-READINGS
Module 2A: Derivatives Markets
XXXXXXXXXXProf Menachem Brenner
March 7 – 9, 2021 (Sun - Tue)
Options, Futures, and Other
Derivatives, John Hull (Textbook)
Hull, Chapters 1 and 2, pp XXXXXXXXXX, 126-
129, pp 49-64, Chs. 10 &12, pp XXXXXXXXXX.
Pre-readings: Derivatives
G1 – G9
Pre-readings: Futures
F1 – F9; ETF1
Pre-readings: Options
O1 – O18
Please jot down 1 - 2 main themes in every article for in-class discussion.
Market Tracking:
You are expected to follow the markets on a daily basis from the day that you receive the first material
egarding this Module, so we could discuss recent developments in class. In particular, you should
pay attention to ‘fair value’ of SPX and NDX, HSI futures and implied volatility from index