FINANCE Risk Management (Exam) S1
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FINANCE Risk Management (Exam)
1 Company X and Company Y have been offered the following fixed and floating borrowing rates:
|
Fixed Rate |
Floating Rate |
Company X |
3.5% |
3-month LIBOR plus 10 bp |
Company Y |
4.5% |
3-month LIBOR plus 30 bp |
Suppose that Company X borrows fixed and Company Y borrows floating first. If they then enter into an interest rate swap contract with each other where the apparent benefits are shared equally, what is company X’s effective borrowing rate?
Select one alternative:
0 3-month LIBOR minus 30 bp
0 3.1%
0 3-month LIBOR minus 10 bp
0 3.3%
Maximum marks: 3
2 Which of the following can describe an interest rate swap?
Select one alternative:
0 A portfolio of forward rate agreements
0 An agreement to exchange interest at a fixed rate for interest at a floating rate
0 An exchange of a fixed rate bond for a floating rate bond
All of the other answers
Maximum marks: 3
3 When expected dividends of the underlying stock increases with all else remaining the same, which of the following is true about calls and puts written on the stock?
Select one alternative:
0 Both calls and puts increase in value
0 Calls increase in value while puts decrease in value
0 Puts increase in value while calls decrease in value
0 Both calls and puts decrease in value
Maximum marks: 3
4 Which of the following most precisely describes the trading strategy where an investor sells a 3- month call option and buys a one-year call option, where both options have a strike price of $100 and the underlying stock price is $75?
Select one alternative:
0 Bear Spread
0 Diagonal Spread
0 Calendar Spread
0 Bull Spread
Maximum marks: 3
5 A trader creates a butterfly spread with put options with strike prices $60, $64, and $68 by trading a total of 4 (buying and selling combined) put options . The option prices are $12, $13, and $16.
What is the maximum profit (after the cost of the options is taken into account) from the butterfly spread?
Select one alternative:
○ $2
○ $1
$3
○ $4
Maximum marks: 3
6 Consider a European call option on a non-dividend-paying stock when the stock price is $52, the strike price is $50, the time to maturity is 6 months , and the continuously compounded risk-free interest rate is 12% per annum . The option is currently trading at $4 each. What is your arbitrage strategy, if there is any?
Select one alternative:
0 No arbitrage opportunity is present based on the given information
0 Short share, borrow $47.09, buy call
0 Long share, borrow $47.09, short call
0 Short share, lend $47.09, buy call
Maximum marks: 3
7 Which of the following describes a situation where an American put option on a stock becomes more likely to be exercised early, other things being equal?
Select one alternative:
0 Expected dividends increase
0 Interest rates decrease
0 The stock price volatility decreases
The stock price increases
Maximum marks: 3
8 Which of the following is true for a one-year call option written on a stock that pays dividends every three months?
Select one alternative:
0 It can be optimal to exercise the option immediately after the last ex-dividend date 0 It can be optimal to exercise the option immediately after the first ex-dividend date
None of the other answers
It is never optimal to exercise the option early
Maximum marks: 3
9 Which of the following is NOT true about gamma?
Select one alternative:
A big positive value for gamma indicates that a big movement in the asset price in either direction will lead to a loss for a long position
The magnitude of gamma is a measure of the curvature of the portfolio value as a function of the underlying asset price
A long position in either a call or a put has a positive gamma
A highly positive or highly negative value of gamma indicates that a portfolio needs frequent rebalancing to stay delta neutral
Maximum marks: 3
10 Which of the following is true for a European put and a European call option written on the same underlying asset with the same exercise price and expiry?
Select one alternative:
The vega of the European put equals the vega of the European call
The vega of the European put equals minus the vega of the European call
0 The delta of the European put equals minus the delta of the European call
0 The delta of the European put equals the delta of the European call
Maximum marks: 3
11 Consider the following European options all written on Stock A with the same expiry:
Name Type Exercise Price Price (Premium)
Put 21
Call 25
Call 27
Put
Call
Call
$21
$25
$27
$2.1
$3.9
$3.1
Your option trading strategy would buy two put options with K = $21 (2 × Put 21’s ), buy one call option with K = $25 ( 1 × Call 25), and short one call option with K = $27 ( 1 × Call 27).
What is the break-even price of Stock A for the strategy at the expiry? In other words , compute the price of Stock A at the expiry where the profit from your option trading strategy would be zero.
NOTE: Final answer should be expressed in dollars rounded to the nearest tenth - for
example, enter $1.23 as $1.2. Intermediate results should not be rounded to less than 8 decimal places unless instructed otherwise.
$
Maximum marks: 6
12 Suppose that the spot price of one British Pound (GBP) is 1.2 U.S. Dollar (USD) and the GBP to USD exchange rate has a return standard deviation of 20% per annum . The risk-free rate
(continuously compounded) in the U.K. is 4% while that in the U.S. is 3% p.a.
Calculate the value of a two-year European call option on British Pound with an exercise price of 1.0 USD using the Garman– Kohlhagen model (GKM model).
NOTE: Final answer should be expressed in USD rounded to the nearest ten thousandth
(0.0001) - for example, enter 1.234567 USD as 1.2346 USD. Intermediate results should not be rounded to less than 8 decimal places unless instructed otherwise.
USD
Maximum marks: 7
13 A financial institution has the following portfolio of over-the-counter options on XYZ stock.
Type |
Position |
Delta of Option |
Gamma of Option |
Vega of Option |
Call |
-600 |
0.4 |
1.5 |
1.8 |
Call |
-400 |
0.8 |
0.5 |
0.2 |
Put |
-3,000 |
-0.3 |
0.8 |
0.7 |
Call |
-500 |
0.7 |
0.6 |
1.4 |
A short position is signed negative – for example, a position of “-600” indicates 600 options short- sold. All the options in this question have a contract size of 1 share.
A traded option on XYZ stock is available with a delta of -0.3, a gamma of 1.0, and a vega of 0.8. You would like to make the portfolio both gamma neutral and delta neutral by taking additional positions in the traded option and XYZ stock itself.
What position in XYZ stock should you take?
NOTE: Denote a long position (buy) with a positive number and a short position (short-sell) with a negative number - for example, to indicate a short-selling of 12 shares , enter - 12 shares . Final answer should be expressed in shares rounded to the nearest whole number - for example, enter 12.345 shares as 12 shares . Intermediate results should not be rounded to less than 8 decimal places unless instructed otherwise.
shares
Maximum marks: 7
Question 14. (9 marks)
A financial institution is reviewing an existing currency swap with company ABC Ltd that was previously entered into. Under the terms of the swap (these terms were agreed at the commencement of the swap):
- The financial institution receives interest once each year (in arrears) at 4% per annum fixed in United States Dollars (USD).
- The financial institution pays interest once each year (in arrears) at 7% per annum fixed in New Zealand Dollars (NZD).
- Both rates above are simple interest rates .
- The initial principal amounts of the swap were NZD 9.0 million and USD 6.0 million.
Assume that current interest rates for all maturities are:
NZD interest rates 5.00% p.a. continuously compounded
USD interest rates 3.00% p.a. continuously compounded The current exchange rate today is NZD 1.00 = USD 0.6000.
The swap has a remaining life of 2.5 years today. What is the current market value of the swap in USD from the perspective of the financial institution?
(Total for the Question: 9 marks)
Question 15. (18 marks)
Entries in the table below represent American call and put options prices on the stock of ABC. The current stock price of ABC is $22. ABC does not pay dividends and the risk-free interest rate is 10% p.a. for all maturities (continuously compounded).
|
Column A Expiry: 0.5 year |
Column B Expiry: 1 year |
Column C Expiry: 2 years |
|
Exercise Price K=$20 K=$22 K=$24 |
American Calls
$3.5 $4.0 Not traded |
American Puts Not traded Not traded $1.5 |
American Calls Not traded $6.5 Not traded |
American Puts Not traded $7.0 Not traded |
a. Consider the options in Column A. Are the 0.5-year American call options with K = $20 and K = $22 mispriced? If so, clearly explain why. (3 marks)
b. Consider the option in Column B. Is the 1-year American put option with K = $24 mispriced? If so, clearly explain why. (3 marks)
c . Consider the options in Column C. Are the 2-year American call and put
options with K = $22 mispriced? If so, set up an arbitrage strategy and verify that the strategy generates an arbitrage profit by showing its net cash flows now and in the future. ( 12 marks)
(Total for the Question: 18 marks)
Question 16. (23 marks)
A non-dividend paying stock is currently trading at $30. There are a European put
option and an American put option written on this stock that have the same exercise price of $35 and the same expiry in 0.6 year – that is , the only difference is one being European and the other being American. The continuously compounded risk-free
interest rate is 8% p.a. and the annualized stock return standard deviation is 30%.
In addition to the put options , any amount of the underlying stock as well as risk-free bonds can also be bought or short-sold. Use the Binomial Option Pricing model with the life of the options divided into three periods for the question.
a. Compute the three-period binomial option price of the European put option. ( 10 marks)
b. Based on your answer in part a), what is the value of the right of early exercise (early exercise premium) of the American put option? (4 marks)
c . You found that the current market price of the European put is $4. Based on your answer in part a), you determined that an arbitrage opportunity is
available. In order to take advantage of the opportunity, you would form a
portfolio consisting of positions in the stock and risk-free bonds that replicates the European put in part a). What is the replicating portfolio now (at time 0)? (6 marks)
d. Do you expect your answer in part c) to be different at time 1 (0.2 year from now)? Why or why not? Explain in words . No calculation is necessary. (3 marks)
(Total for the Question: 23 marks)
2023-10-23