[FINANCIAL DERIVATIVES
PRACTICE QUESTIONS ]
Chapter 1: Introduction to Derivatives
1. An investor receives $1,100 in one year in return for an investment of $1,000 now. Calculate
the percentage return per annum with:
(a) Annual compounding
(b) Semiannual compounding
(c) Monthly compounding
(d) Continuous compounding.
2. Suppose that zero interest rates with continuous compounding are as follows:
Maturity
Rate
(months) (% per annum)
3
6.0
6
6.2
9
6.3
12
6.5
15
6.7
18
7.0
•
Calculate forward interest rates for the second, third, fourth, fifth, and sixth quarters.
•
The investor intends to invest 1,000 USD at the end of month 3. How much will he
receive after 1 year?
3. A deposit account pays 12% per annum with continuous compounding, but interest is
actually paid quarterly. How much interest will be paid each quarter on a $10,000 deposit?
4. Suppose that 6-month, 12-month, 18-month, 24-month, and 30-month zero rates are,
respectively, 4%, 4.2%, 4.4%, 4.6%, and 4.8% per annum, with continuous compounding.
PRACTICE QUESTIONS ]
[FINANCIAL DERIVATIVES
Estimate the cash price of a bond with a face value of 100 that will mature in30 months and
pays a coupon of 4% per annum semiannually.
5. You would like to speculate on a rise in the price of a certain stock. The current stock price
is $29 and a 3-month call with a strike price of $30 costs $2.90. You have $5,800 to invest.
Identify two alternative investment strategies, one in the stock and the other in an option on
the stock. What are the potential gains and losses from each if the stock price increases to a)
$36 per stock and b) decreases to $27 per stock at the end of 3 months ?
6. You have $5,200 to invest and you would like to speculate on a rise in the price of a certain
stock. The current stock price is $52; the futures stock price is $55, each futures contract is for
the purchase of 50 stocks, initial margin for each futures contract is $20. A 3 month call with
a strike price of $55.5 costs $4. Each option is for the purchase of 50 stocks.
1. Identify alternative investment strategies
2. What are the potential gains and losses from each strategy if the stock price at the
end of 3 months a) increases to $60 per stock and b) decreases to $52 per stock
3. Which strategies will you choose ?
7. Trung Nguyen coffee company expects to receive 2 million USD for exporting coffee to US
in the next three month. The three month forward rate is 22,000 USD/VND. A 3 month put
option to sell USD with a strike price of 23,500 costs 200,000 VND. One option is to sell 100
USD.
1. What risks is Trung Nguyen exposed to ?
2. What strategies the company could do to hedge the risks ? What are the potential
outcomes from each strategy if the 3 month exchange rate is: (a) 25,000 or (b) 20,000
3. Instruct the company what they should do to hedge the risks
[FINANCIAL DERIVATIVES
PRACTICE QUESTIONS ]
Chapter 2: Futures
1. Suppose that you enter into a 6-month forward contract on a non-dividend-paying stock
when the stock price is $30 and the risk-free interest rate (with continuous compounding) is
12% per annum. What is the forward price ?
2. A 1-year long forward contract on a dividend-paying stock is entered into when the stock
price is $40, a dividend of 2$ is expected to be paid at the end of every six month and the riskfree rate of interest is 10% per annum with continuous compounding.
a) What is the forward price ?
b) Six months later, the price of the stock is $45 and the risk-free interest rate is still
10%. What is the 6 month forward price?
3. A stock index currently stands at 350. The risk-free interest rate is 8% per annum (with
continuous compounding) and the dividend yield on the index is 4% per annum. What should
the forward price for a 4-month contract be ?
4. The risk-free rate of interest is 7% per annum with continuous compounding, and the
dividend yield on a stock index is 3.2% per annum. The current value of the index is 150. What
is the 6-month forward price ?
5. The spot price of silver is $15 per ounce. The storage costs are $0.24 per ounce per year
payable quarterly in advance. Assuming that interest rates are 10% per annum for all
maturities, calculate the forward price of silver for delivery in 9 months.
6. The 2-month interest rates in Switzerland and the United States are, respectively, 2% and
5% per annum with continuous compounding. The spot price of the Swiss franc is $0.8000.
The forward price for a contract deliverable in 2 months is $0.8100. What arbitrage
opportunities does this create ?
7. A stock is expected to pay a dividend of $1 per share in 2 months and in 5 months. The
stock price is $50, and the risk-free rate of interest is 8% per annum with continuous
compounding for all maturities.
a) What is the forward price in a 6-month forward contract ?
PRACTICE QUESTIONS ]
[FINANCIAL DERIVATIVES
b) Three months later, the price of the stock is $48 and the risk-free rate of interest is
still 8% per annum. What is the 3-month forward price ?
8. A 6-month long forward contract on $1,000 is entered into when the exchange rate is 20,000
USD/VND and the risk-free rate of interest is 6% per annum in Vietnam and 3% per annum
in US with continuous compounding. Assume that the risk-free interest rate is constant.
a) What are the 6-month forward price ?
b) Three months later, the exchange rate is 22,000 USD/VND. What is the forward
price of a 6-month contract ?
9. A 9-month short forward contract on $1,000 is entered into when the exchange rate is
19,000VND/USD and the risk-free rate of interest is 7% per annum in Vietnam and 4% per
annum in US with continuous compounding. Assume that the risk-free interest rates are
constant.
a) What is the 9 month forward price ?
b) Three months later, the exchange rate is 21,000VND/USD. What is the 6 month
forward price ?
10. On January 1, 20X1 a company entered into short position of a FRA contract in which the
company would receive interest at 7% per year on the principal of $10 million for a period of
6 months. The contract starts after a period of 2 years. On January 1, 20X3 the SOFR is
6%/year, compounded semiannually. Determine the cashflow exchange on the same date
11. On January 1, 20X1 a FRA contract was signed between two parties in which the seller
would receive interest at 6% p.a on the principal of $10 million for a period of 6 months. The
contract starts after a period of 1 year. On January 1, 20X2 the SOFR is 5.5%/year,
compounded semiannually. What is the payoff of FRA to the seller/buyer ?
[FINANCIAL DERIVATIVES
PRACTICE QUESTIONS ]
Chapter 3: FUTURES
1. Suppose that you enter a short futures contract to sell July silver for $17.20 per ounce. The
size of the contract is 5,000 ounces. The initial margin is $4,000, and the maintenance margin
is $3,000.
- What change in the futures price will lead to a margin call?
- What happens if you do not meet the margin call?
2. A trader buys two July futures contracts on orange juice. Each contract is for the delivery
of 15,000 pounds. The current futures price is 160 cents per pound, the initial margin is $6,000
per contract, and the maintenance margin is $4,500 per contract.
- What price change would lead to a margin call?
- Under what circumstances could $2,000 be withdrawn from the margin account?
3. A company enters a short futures contract to sell 5,000 bushels of wheat for 450 cents per
bushel. The initial margin is $3,000 and the maintenance margin is $2,000.
- What price change would lead to a margin call?
- Under what circumstances could $1,500 be withdrawn from the margin account?
4. An investor bought 3 December coffee futures contracts on the CME market at a price of
$150/ton. The contract scale is 100 tons/contract. Each contract has an initial margin of $2,000
and a maintenance margin of $1,500. At the end of the day, the futures price closed at $152/ton.
Calculate the balance of the investor's margin account at the end of the trading day.
5. The spot price of silver is $15 per ounce. The storage costs are $0.24 per ounce per year
payable quarterly in advance. Assuming that interest rates are 10% per annum for all
maturities, calculate the futures price of silver for delivery in 9 months.
6. An index is 1,200. The three-month risk-free rate is 3% per annum and the dividend yield
over the next three months is 1.2% per annum. The six-month risk-free rate is 3.5% per annum
and the dividend yield over the next six months is 1% per annum. Estimate the futures price
of the index for three-month and six-month contracts. All interest rates and dividend yields are
continuously compounded.
PRACTICE QUESTIONS ]
[FINANCIAL DERIVATIVES
7. A short contract on 1-million-kilogram copper is signed on 01/01/20X0, the agreed price is
the market price on 01/06/20X0. The current copper price on 01/01/20X0 is $10/kg, the June
futures copper price is $9/kg (each futures contract is for the purchase of 1,000 kg)
- What could the copper producer do to hedge the risk?
- What are the incomes of the copper producer in the 2 following strategies, and
compare with his income if he does not hedge the risk with futures?
a) The copper price on 01/06 is $7.50/kg
b) The copper price on 01/06 is $10.50/kg
8. VinaCafe needs 100,000 pounds of coffee on 01/09/20X0. The current coffee price on 01/06
is $20/pound. The September futures coffee price is $18/pound (each futures contract is for
the purchase of 25,000 pounds.
- What could VinaCafe do to hedge the risk?
- What are the costs of VinaCafe in the 2 following strategies, and compare with his
cost if he doesn’t hedge the risk with futures?
a) The coffee price on 01/09 is $19.50/pound
b) The coffee price on 01/09 is $17/pound
[FINANCIAL DERIVATIVES
PRACTICE QUESTIONS ]
CHAPTER 4: SWAPS
1. Companies A and B have been offered the following rates per annum on a $ 20 million five-year
loan:
Fixed rate
Floating rate
Company A
12%
Libor+0.1%
Company B
13.5%
Libor+0.6%
Company A requires a floating-rate loan; Company B requires a fixed-rate loan. Design a swap that
will net a bank, acting as an intermediary, 0.1% per annum, and will appear equally attractive to both
companies.
2. Companies A and B have been offered the following rates per annum on a $ 20 million five-year
loan:
Fixed rate
Floating rate
Company A
12%
Libor+0.1%
Company B
13.5%
Libor+0.6%
Company A requires a floating-rate loan; Company B requires a fixed-rate loan. Setting up a swap
without a financial intermediary and the gain from the swap is equally shared among the two parties.
3. Company X wishes to borrow a USD loan at a fixed interest rate. Company Y wishes to borrow a
Japanese yen loan at a fixed interest rate. The amounts required by the two companies are roughly the
same at the current exchange rate. The companies have been quoted the following interest rates, which
have been adjusted for the impact of taxes:
JPY
USD
Company X
5.0%
9.6%
Company Y
6.5%
10.0%
Design a swap that will net a bank, acting as an intermediary, 50 basis points per annum and will
appear equally attractive to both companies and ensure that all foreign exchange risk is assumed by
the bank.
1.
Both Company A and B wish to borrow 10 billion VND for 5 years, paying interest every 6
months. The market interest rates are as follows:
Company A
Fixed rate
Floating rate
7%
Libor
Requirement
Floating rate
[FINANCIAL DERIVATIVES
PRACTICE QUESTIONS ]
Company B
8.5%
Libor+0.5%
Fixed rate
Calculate the benefits of the 2 companies participating in a swap contract which will net a bank, acting
as a financial intermediary, a 0.2% fee, and the gain from the swap is equally shared among the two
parties.
2.
On January 1, 20XX, PN Company, and DT Company signed a swap contract with 100 billion
VND capital, in which the agreement was that PN Company would receive a fixed interest rate of
6.50%/year and pay DT Company Libor interest rate semiannually. The 6-month Libor interest rates
were as follows:
Libor (%per annum)
1/1/20XX
5.25%
1/7/20XX
5.50%
Determine PN Company’s net cash flow in the swap contract after 6 months.
6. Company A, a British manufacturer, wishes to borrow US dollars at a fixed interest rate. Company
B, a US multinational, wishes to borrow sterling at a fixed interest rate. They have been quoted the
following rates per annum (adjusted for differential tax effects):
Sterling
US dollars
Company A
11.0%
7.0%
Company B
10.6%
6.2%
Design a swap that will net a bank, acting as an intermediary, 10 basis points per annum, and that will
produce a gain of 15 basis points per annum for each of the two companies.
7. Today, Sun Company signed a 2-year currency swap contract with Moon Bank. It involves
exchanging interest at 10% on £20 million for interest at 6% on $30 million once a year. All interest
rates are quoted with annual compounding. Determine Sun company’s cashflows of the currency swap
contract.
PRACTICE QUESTIONS ]
[FINANCIAL DERIVATIVES
CHAPTER 5: OPTIONS
1. You purchase an underlying asset priced at $77 and write a call option on it with an exercise price
of $80. The call costs $6.
a. Determine: payoff; maximum gain; maximum loss; breakeven price.
b. Draw the payoff graph of this strategy.
2. You purchase an underlying asset priced at $57 and long a put option on it with an exercise price of
$55 and selling at $3.
a. Determine: payoff; maximum gain; maximum loss; breakeven price.
b. Draw the payoff graph of this strategy.
3. The price of stock is $28 and the price of a three-month European call option on the stock with a
strike price of $27 is $1.3. The risk-free rate is 4% per annum. What is the intrinsic value and time
value of this call option
4. An investor purchases call options to buy 1,000 shares with an exercise price of $143/share. The
call costs $5/share. Assume that at maturity, the market price of the stock is $160. Draw a graph and
determine the investor's payoff.
5. The price of gold is 1,500 USD/ounce and the price of a six-month gold call option with a strike
price of 1,490 USD/ounce is 2,500 USD. The Call Options contract size is 100 ounces of gold. Is it
an ITM, ATM, or OTM option? What is the intrinsic value and time value of this call option?
6. Suppose that put options on a stock with strike prices of $30 and $35 cost $4 and $7, respectively.
How can the options be used to create (a) a bull spread and (b) a bear spread? Construct a table that
shows the profit and payoff for both spreads.