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OFS-P07
(PGDM 2007-09 : Term-V)

OPTION, FUTURES, AND SWAP
3.0 Credits
Instructor: Banikanta Mishra

Course Objective: This course exposes you to the three basic derivative instruments: forward & futures, option, and swap. The focus would be on characterizing the instruments and learning how to value them and how to use them in hedging against risks, protecting investments, and speculating. Derivatives on shares, currency, interest-rte, and commodity would be looked at. Simple and exotic extensions of the basic instruments would be taken up whenever time and opportunity permits. If time permits, innovations involving derivatives would be taken up briefly.

Course Materials: The text for this course is Options, Futures, and Other Derivatives by John Hull (Sixth Edition; Prentice Hall). My handouts and lectures would supplement the book. You may also glance through The New York Institute of Finance Guide to Investing (Simon & Schuster). You may enjoy reading Peter Bernstein’s Against the Gods: The Remarkable Story of Risk (Wiley, 1998), especially if you are contemplating a career in risk-management or derivatives. For cases, you would need to refer to Case Problems in Finance by Carl Kester, Richard Ruback, and Peter Tufano (McGraw Hill International Edition, Twelfth Edition).

Cases: Group solutions to the three cases have to be submitted; each group should have 3-4 students. Detailed instruction on how to write case reports would be provided. (Please inform me as soon as you have formed your group.)

Practice Questions: For each week, I have suggested some chapter practice questions (PQs) from the book. You should not submit solutions to PQs; but, if time permits, you should work on the PQs. I may occasionally discuss answers to selected PQs. You should also work out the attached Special Practice Questions, though they do not necessarily represent the shape of things (questions) to come.

Attendance and CP (Class Participation): All students are expected to take an active part in class discussions. It is not enough for a student to do well in the above-cited quizzes/examinations and assignments. Class-participation is an integral component of the learning process. Therefore, I would urge you to come well-prepared to the class, to answer questions when called upon to do so, and to raise interesting issues for discussion. For each class, I would give you a score between 0 and 10. If you miss a class or are inactive, you would get 0 for that class. Each class carries a weight of around 0.50%; thus, the total weight on CP for the scheduled 20 classes is 10%.

Grade: Total weight for the course is distributed over three cases (5% each x 3 = 15%), midterm exam (35%), final exam (40%), and participation in the 20 classes (0.50% x 20 = 10%). Your performance in the course is determined by your weighted-average-score in percentage (WASP) in the above.

Grading Scale: Your course-grade would be determined as per the following rule.

If your WASP is less than 70, you may get a grade below C (that is, D+, D, or F).
If your WASP is 70 or more OR in the top 80% of class, then you are guaranteed a C or above.
If your WASP is 80 or more OR in the top 40% of class, then you are guaranteed a B or above.
If your WASP is 90 or more OR in the top 10% of class, then you are guaranteed an A or above.

Examinations: These closed-book examinations would typically have both conceptual questions and numerical problems (short, medium, long). I would provide you with formulae; you are not allowed to bring any formula-sheet to the examinations. Examinations would last for around 90-180 minutes. There will be no make-up examination, unless you miss the regular one due to a proved “emergency”.
Some Basic Examination Rules: You would be given either a question-cum-answer paper or a question paper with an attached answer-paper. In the former case, you would be given a specific amount of space following each question for writing your answer. In the latter, you would be given a specific total number of pages to write your answers in; you should use both sides of each sheet and show your answers in ascending order (answer to Q.1 first, followed by answer to Q2, and so on), leaving half-inch gap between your answers. In all cases, leave half-inch margin on both left and right sides. Read instructions, if any, on the question/question-cum-answer book; if an instruction therein conflicts with one given here, then it overrides the one given here. If not specifically asked to use a pen, you may use either pen or pencil. Write legibly; if I cannot read what you have written, I will not give you any points for the relevant portion. Unless merely asked to tick the right answer, explain clearly all your derivations and answers; if no explanation is given, no credit will be given for merely ticking or jotting down the correct answer. Be precise; clumsy writing and imprecise or unnecessarily lengthy answers will be penalized. You are not allowed to seek any clarifications from anyone (not even your instructor) during examinations; if a question is wrong or unclear, just state why the question is wrong/unclear and, if possible, make an assumption and answer the question. If you are found to be justified doing what you did, you will get full points; or else, you would receive less (even zero). In all your assignments (examinations, reports, quizzes, projects), mention only your roll-number, not your name. If you write your name, you would be heavily penalized.

Code of Ethics: You must abide yourself by the (unwritten?) Code of Ethics for Students. For individual assignments/examinations, it is unethical to seek any direct help from others, whether or not you finally make use of the help. Discussions among individual students (except in the examination hall or class-room) are, of course, always encouraged. But, the final report or solution should be totally in the individual’s own style and language; any form of copying from one another or from any outside source is forbidden. Your basic purpose should be to learn, without resorting to any unfair means for getting a higher score or QPI. If you resort to any unfair means, you would receive an F in the whole course, not merely in the component for which you violate the code.

Feedback: Feedback is always useful, even for the most seasoned veteran. In that spirit (but, of course, without claiming to be either seasoned or a veteran), I would request you to submit the midterm-evaluation on the date mentioned at the top of the midterm-evaluation-form (included). The final evaluation-form, which is different from the "official" one you would receive from the Dean's Office, also asks some specific questions regarding topics and cases (which are not touched upon by the official form). I would be thankful if you submit it to me on the day of the final examination (just before the exam). I would also request you to give me continuous “informal” feedback; toward this, the class may like to form a “focus group” (consisting of 6-7 students from the class with diverse backgrounds) that continuously interacts with the students and informs me about their problems, if any, with the course.

Indicative Schedule: The Indicative Schedule on the next page gives you an idea about the chronological sequence of topics I plan to cover and the amount of time I plan to spend on each topic. It is by no means binding. I would try my best to ensure that you understand a topic well before moving on to the next topic. Based on my past experience, I, of course, believe that we shall be able to cover most, if not all, topics mentioned in the Indicative Schedule.

Concerns and Contact Details: Though I am usually available in my office, please check beforehand. I also may come in for a few hours on weekends (the timings vary) and would try to give you a weekend appointment if you need one. You can, of course, always reach me by e-mail at my XIMB-id or at banikanta@hotmail.com. If you have any concerns regarding the course, you should discuss them with me. But if there are some concerns that you cannot discuss with me or regarding which you fail to get any satisfactory result after discussing with me, you should approach the A&F Area Coordinator.
I hope that I live up to your expectation (of teaching well) and you up to mine (of working hard).
I also hope that you enjoy the course and get the value of your time and money spent on it.

Indicative Schedule
Session
Topics Covered
Chapter(s)
Chapter Practice Questions
1
Forward, Futures, Option, Swap
1 - 2
1.15, 1.19, 1.23, 1.25,
2.3, 2.15, 2.24
2
Hedging with Futures
3
3.6, 3.7, 3.18
3-4
Interest Rates
4
4.5, 4.7, 4.11, 4.16
5
Determination of Forward Prices
5
5.10, 5.11, 5.14, 5.17
6
Interest-Rate Futures
6
6.4, 6.8, 6.13, 6.15
7-8
Swaps
7
7.1, 7.5, 7.9, 7.11
9
Options Market
8
8.1, 8.2, 8.9, 8.12
10
Properties of Stock Options
9
9.7, 9.12, 9.15
11
Binomial OPM and Risk Neutral Valuation
11
11.1, 11.4, 11.11, 11.12
12
Black-Scholes OPM
12-13
13.4, 13.7, 13.13
13
Index, Currency, Futures Option
14
14.7, 14.9, 14.25, 14.30
14
The Greeks and Delta Hedging
15
15.2, 15.9, 15.10, 15.22
15
Trading Strategies With Options
10
10.7, 10.10, 10.11
16
Advanced Topics in Options
Lecture
17
Case-1 Sally Jameson
18
Case-2: Student Educational Loan Fund
19
Case-3: Arundel Partners
20
REVIEW
ALL
Special Practice Questions
(Some Taken From the Text)
(NOT in chronological order, that is, not in the order topics are covered,
to test your ability to ferret out the relevant concept)

1. The value of the index is now 1000. Three-month at-the-money calls are now selling for Rs.30.00. The stated interest-rate is 10%, which is continuously compounded. How can you achieve portfolio-insurance with and without a long position in the index-tracking-portfolio? What would be the required investment now and what would be the cash flows at the end of three months? What would be your cash flow at the end of three months if you have a naked long position in the index-tracking-portfolio? Why are the earlier strategies called "insurance", and what is the analogue of insurance-premium in these strategies?

2. You have a portfolio currently valued at Rs.80,00,000. Its beta is 1.25. Market-index is currently at 500. At-the-money index put and call have deltas of -0.8 and +0.2 respectively. These put and call have gammas of 0.0375. If exercised, index options are settled by paying the holder 100 times the difference in the index-level and the strike-level. What and how many options would you buy today to hedge your portfolio against a market downturn? What would happen to your portfolio value if the index falls by 4% just after you have gone for the hedge?

3. At present $1 = Rs.40. But, $ is expected to go up to 50 or fall to 45 by the year-end. You can currently buy $ forward @Rs.48. You are considering the alternative of a call on $ at strike of 49. What is the maximum you would be willing to pay for this call? [Risk-free rupee rate is currently 20%.] Follow the simplest possible approach.

4. Current price of ABC's shares is Rs.303. You feel that you can make a lot of money if you buy the share today and sell it at the end of one month. Current interest-rate is 1% per month, compounded monthly. You have three choices open to you: (1) Buy the share for cash today and sell it at the end of the month, (2) Buy the share with 0% margin (i.e. borrow the full amount needed to buy) and sell the share at the end of the month, (3) Buy 1-month ATM (at-the-money) call on ABC shares (premium=Rs.15.00) and sell 1-month ATM put on ABC shares (premium=Rs.12.00). Derive the cash flows for each of the three choices. Are the three strategies equivalent? [Use discrete-time equations.]

5. A financial institution has the following portfolio of over-the-counter options on sterling:

TypePositionOption DeltaOption GammaOption Vega
Call-1,0000.502.21.8
Call-5000.800.60.2
Put-2,000-0.401.30.7
Call-5000.701.81.4

A traded option is available which has a delta of 0.6, a gamma of 1.5, and a vega of 0.8.

a) What position in the traded option and in sterling would make the portfolio both gamma neutral and delta neutral?
b) What position in the traded option and in sterling would make the portfolio both vega neutral and delta neutral?

6. The price of an American call on a non-dividend-paying stock is Rs.4. The stock price is Rs.31, the strike price is Rs.30, and the expiration date is three months. The risk-free interest rate is 8 percent. Derive upper and lower bounds for the price of an American put on the same stock with the same strike price and expiration date.

7. The price of a European call, which expires in six months and has a strike price of Rs.30, is Rs.2. The underlying stock price is Rs.29, and a dividend of Re.0.50 each is expected at the end of two months and at the end of five months. The term structure is flat, with the risk-free APR being 10 percent, which is continuously compounded. What is the price of a European put option that expires in six months and has a strike price of Rs.30?

8. Assume that the risk-free APR is 11%, which is continuously compounded. Given below is data for the price (in rupees) of ABC's shares for the last 10 days (two weeks), with the last number being today's closing price.

208 220 213 202 197 190 203 205 202 200

The corresponding level of the index for these 10 days are as follows.

1999 2050 2020 2000 2005 1898 1950 1970 1960 1950

Determine the premium for a three-month ATM call on ABC's share. Determine the price of the corresponding put. Draw the payoff diagram for a long straddle involving these two.

9. Take the question above. Determine the premium for a three-month ATM call on the index. If exercised, each call gives the holder 100 times the difference between the index-level and the pre-specified strike-level. Determine the price of the corresponding put. If you buy the call and sell the put, is it equivalent to going long in the index today and unwinding it at the end of three months? Determine the delta and gamma for the above call and put, and explain what they mean.

10. Take the two questions above. Assume that you are just now going to invest Rs.200,000 in ABC shares and are going to hedge it for three months with ATM index options. What and how many index options would you need to go for? What would happen to your above portfolio if the market falls by 2%? Can you replicate this hedged investment using the index-call? How?

11. You need 1000 widgets per month for the next twelve months. Market expects the price of widgets to continuously fall from its current level of Rs.200 to Rs.140 by the year-end. You, however, believe that the price would fall quite fast to Rs.170 within six months and remain there till year-end. You can enter into a six-month swap to buy widgets @ Rs.180, but you find the price a bit high. What can you do to bring down your cost of buying widgets?

12. Show that, if futures contracts were marked to market with the present-values (of the differences between the futures prices on that day and the previous day), the futures price would equal the forward price every day. How do you reconcile this with the fact that, even when futures contracts are marked to market in the traditional way, futures price still equals forward price on the day before maturity?

13. An asset is now selling for Rs.65. It is expected that, at the year-end, it would be selling for either Rs.80 or Rs.60. Risk-free rate is 20%; this is the annually-compounded EAR. What should be the premium for a one-year call on the asset at a strike of Rs.70? Derive this both using the Binomial Option Pricing Model and the Risk-Neutral Valuation Model (that is assuming that we are in a risk neutral world). Why does the option premium remain unchanged in a risk-averse world?

14. Suppose that sterling-U.S. dollar spot and forward exchange rates are as follows. Spot: 1.8470 90 day forward: 1.8381, 180-day forward: 1.8291. What opportunities are open to an American investor in the following situations? a) A 180-day European option to buy £1 for $1.80 costs $0.0250, b) A 90-day European put option to sell £1 for $1.86 costs $0.0200.

15. Explain the concept of “hedge ratio”. Using this concept, explain the technique of duration-based hedging. If the term-structure is flat at 12%, and you plan to hedge your portfolio of 250 units of Rs.100-par six-month TB by taking a position in three-month TBs, what position should you take? What would happen to your portfolio value if interest-rate rises by 0.5%? How much does the hedging cost you?

16. Three years back, your company issued 5-year floating-rate Re-bonds at 50 basis points over Mumbai Inter-Bank Offer Rate (MIBOR), though many bankers advised you to go for $-bonds at $-LIBOR+70bp. At that time MIBOR was 11.5% and $-LIBOR was 5.3%. You have noticed that Re has been steady against $ in the recent past. $-LIBOR is 5% now, which is 5% below Re-MIBOR. Everyone expects that $-interest-rate would rise and Re-interest-rate would fall. What kind of swap(s) can you enter into to exploit this market belief and transform your loan into a cheaper one? Does it matter whether you expect Re to remain steady against $?

17. The current price of a stock is $94, and three-month call options with a strike price of $95 currently sell for $4.70. An investor who feels that the price of the stock will increase is trying to decide between buying 100 shares and buying 2,000 call options (20 contracts). Both strategies involve an investment of $9,400. Which is better? How high does the stock price have to rise for the option strategy to be more profitable?

18. An Indian company that imports aluminum has just issued a bond with a “stated” par value of Rs.1000. To protect it against the exchange-rate appreciation, it has stipulated that, if the exchange-rate (rupees per dollar) on the maturity-date exceeds 40, it would pay only Rs. [1000 – (N x 25)] in par (where N is the amount by which the exchange-rate exceeds 40) subject to the condition that under no circumstances shall the bondholder receive less than 75% of the par-value. Show that the bond is a combination of a straight bond and two calls, one long and the other short. What are the strike prices of the long and the short call options?

19. Bid-ask prices for rice from the rice-dealers are currently quoted at Rs.1,500-Rs.1,600 per quintal. Rice can be stored for a year by paying the storage-provider, at the end of the year, 1% of the initial (beginning of the year) inventory-value. Storage, however, leads to a loss of around 4% of the rice due to handling. What must be the range for the year-end forward-price to rule out arbitrage? [The banks have quoted their borrowing (deposit taking)-lending rates at 15%-16%.]

20. Companies A and B face the following interest rates:

Form of FinancingCost to ACost to B
U.S. dollars (floating rate)
German marks (fixed rate)		LIBOR+ 50bp
5.0%		LIBOR+ 100bp
6.5%

Assume that A wants to borrow dollars at a floating rate of interest and B wants to borrow marks at a fixed rate of interest. A financial institution is planning to arrange a swap and requires a 50 basis point spread. If the swap has to be equally attractive to A and B, what rates of interest will A and B end up paying? [Show the swap completely.]

21. The following table gives ten data-points on monthly changes in the spot price and the futures price for a certain commodity. Calculate the optimal hedge ratio.

Spot price change +0.50 +0.61 -0.22 -0.35 +0.79
Futures price change +0.56 +0.63 -0.12 -0.44 +0.60
Spot price change +0.04 +0.15 +0.70 -0.51 -0.41
Futures price change -0.06 +0.01 +0.80 -0.56 -0.46

22. Suppose that it is February 20, and a treasurer realizes that on July 17 the company will have to issue $5 million of commercial paper with a maturity of 180 days. If the paper were issued today, the company would realize $4,820,000. (In other words, the company would receive $4,820,000 for its paper and have to redeem it at $5,000,000 in 180 days’ time.) The September Eurodollar futures price is currently quoted as 92.00. How should the treasurer hedge the company’s exposure?

23. Current bid-offer interest-rates posted by banks are 1%-1.1% per month and 4.3%-4.5% per quarter. The current forward price for 60-day TBs for the contract expiring at the end of the month is 97.00. Is arbitrage possible? If yes, delineate the whole arbitrage strategy.

24. Given below are current prices of treasury-securities of different maturities. Assuming that continuous compounding is followed, derive the zero rate for each of the given maturity.

Time to Maturity Annual Coupon Rate* Price (as a % of par value)

3 months 0% 96.08
6 months 0% 92.77
1 year 0% 86.94
1.5 years 10% 94.95
2 years 12% 97.43
(* paid semi-annually)

What should be the price of a two-year treasury-security that gives 14% coupon, paid annually?

25. An Indian firm could directly issue $-bonds at a rate 1% higher than $-TB rate, which was 9% in 2001 and is 6% now in 2002. It has issued some $-bonds in 2001 at 10% coupon. These bonds are callable in 2006, and they mature in 2011. Since the firm does not usually like $-exposure, it had entered, at the time of issue, into a currency-swap, whereby it receives $ interest at 10% (of a notional principal equivalent to the face-value of debt issued) and pays Rupees (Rs) at a rate of MIBOR - 25bp (basis points), where MIBOR is the Mumbai InterBank Offer Rate. Now, the firm finds that $ has strengthened against Rs, so that it can enter into a swap right now, whereby it would receive Rs at a rate of MIBOR - 25 bp against payment of only 7% in $. If it goes for this swap and $ strengthens against Rs further, it would enter into a reverse-swap next year, wherein it receives $ at 7% for paying Rs at, say, MIBOR - 10 bp (surely it will cost more than MIBOR - 25 bp). Should the firm enter into the swap right now, or should it go for a forward-swap? Explain your logic in detail, with numbers wherever possible and appropriate.

26. What are the differences between an Average Strike Call and a Look-back Call? Suppose that the market believes that the price of the underlying asset would remain reasonably constant/stable over the life of the option, but you think that the price would steadily fall till the option-maturity, which of the two options would you prefer and why?

27. Assume that Microsoft has a daily standard-deviation of 2%, while the corresponding figure for AT&T is 1%. What is the one week (5 day: Monday to Friday) 95% VAR of a $5 million Microsoft portfolio? What about an AT&T portfolio of the same value? What does this number (for, say, AT&T) mean? What is the figure for a mixed portfolio of $5 million in Microsoft and an equal amount in AT$T?

Midterm Evaluation Form
Prof. Banikanta Mishra: OFS: Sep-Dec 2008
(Please submit to the instructor in the class at the end of the 11th class)

Please evaluate each topic covered so far, using the following scale for amount of time spent (1=too little, 2=less than desired, 3=just right, 4=more than desired, 5=too much) and the following scale for quality of coverage (1=very bad, …5=very good)
a) Risk Management 1 2 3 4 5 1 2 3 4 5
b) Forward 1 2 3 4 5 1 2 3 4 5
c) Futures & MTM 1 2 3 4 5 1 2 3 4 5
d) Options 1 2 3 4 5 1 2 3 4 5
e) Swaps 1 2 3 4 5 1 2 3 4 5
f) Hedging with Futures 1 2 3 4 5 1 2 3 4 5
g) Interest Rates 1 2 3 4 5 1 2 3 4 5
h) Forward Pricing 1 2 3 4 5 1 2 3 4 5
i) Interest Rate Futures 1 2 3 4 5 1 2 3 4 5
j) Swaps 1 2 3 4 5 1 2 3 4 5

Evaluate the below-cited attributes using the following scale: 1=Very Bad, …, 5=Very Good

2. Organized-ness of the Instructor 1 2 3 4 5

3. Clarity of Instruction 1 2 3 4 5

4. Pace of Instruction 1 2 3 4 5

5. Level of Excitement Created by the Instructor 1 2 3 4 5

6. Instructor's Ability to Provide Intuition behind Theories 1 2 3 4 5

7. Perceived "Practical Usefulness" of the Course 1 2 3 4 5

8. Instructor's Patience in Answering your Questions 1 2 3 4 5

9. Instructor's Cooperation in your Learning Process 1 2 3 4 5

10. Instructor's Interpersonal Behavior 1 2 3 4 5


Answer the following questions using the following scale: 1=Not at All, …, 5= Absolutely

11. Did assignments/exam relate to topics covered? 1 2 3 4 5

12. Were the assignments fairly graded? 1 2 3 4 5

13. Were the assignments returned on time? 1 2 3 4 5

Please See Overleaf

Is there anything the Instructor can do to help you learn better?










Is there anything the Instructor can do to make this course an exciting one?










Is there anything the Instructor can do to remove hurdles in your learning in this course?









Is there anything about the Instructor/Course that you would like to see changed?




Final Evaluation Form
Prof. Banikanta Mishra: OFS: Sep-Dec 2008
Please submit on the day of the final examination
(in the exam hall; just after the exam; please leave it on the table)

1. Please evaluate each topic covered so far, using the following scale for amount of time spent (1=too little, 2=less than desired, 3=just right, 4=more than desired, 5=too much) and the following scale for quality of coverage (1=very bad, …5=very good)
k) Options Market 1 2 3 4 5 1 2 3 4 5
l) Properties of Stock Options 1 2 3 4 5 1 2 3 4 5
m) Option Trading Strategies 1 2 3 4 5 1 2 3 4 5
n) Binomial OPM 1 2 3 4 5 1 2 3 4 5
o) Risk Neutral Valuation 1 2 3 4 5 1 2 3 4 5
p) Black-Scholes OPM 1 2 3 4 5 1 2 3 4 5
q) Option on Index, etc. 1 2 3 4 5 1 2 3 4 5
r) Greeks and Delta Hedging 1 2 3 4 5 1 2 3 4 5
s) Exotic Derivatives 1 2 3 4 5 1 2 3 4 5
t) Real Options 1 2 3 4 5 1 2 3 4 5
u) Derivative Disasters 1 2 3 4 5 1 2 3 4 5
v) Innovations using Options 1 2 3 4 5 1 2 3 4 5


2. What is your opinion on cases? (Please skip if no cases were done.)

a) Do you feel this course should have cases? Yes No Uncertain

b) If Yes, how many? 1 2 3 4 5


Evaluate the below-cited attribute using the following scale: 1=Very Bad, …, 5=Very Good

3. Perceived "Practical Usefulness" of the Course 1 2 3 4 5


Answer the following question using the following scale: 1=Not at All, …, 5= Absolutely

4. Did assignments/exams relate to topics covered? 1 2 3 4 5


5. Any other comments (if required, please use the back side)?
Created By: Bijoy Kar on 09/08/2008 at 02:11 PM
Category: PGP-II Doctype: Document

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