Homework 9, FINA 471 Fall, 2011
PROBLEM 1
The current exchange rate is $1.44/€, the euro interest rate is 3.5%, the dollar interest rate is 2%, and the price of a 3month $1.45strike European
put option is $0.12. What is the price of a 3month $1.45strike European call?
A. By putcall parity, C = P + xerfT – KerT = 0.12 + 1.44e0.035*0.25 – 1.45e
0.02*0.25 = $0.1047.
PROBLEM
2 A stock currently sells for $42. The 6month European call option with a strike of $45 has a premium of $2.50, and the
6month European put option with a strike of $45 has a premium of $5.15. The annual continuously compounded interest rate is 2%. What should be the present
value of dividends over the next 6 months? A. By putcall parity, PV(Div) = S – C + P – KerT = 42 – 2.5 + 5.15 – 45e0.02*0.5 = $0.10. (
PROBLEM
3 A stock
currently sells for $42. A 6month European put option with a strike of $45 has a premium of $6.50. Assuming a 2% annual continuously compounded interest
rate and a 4% dividend yield, what should be the price of the associated European call option? B. By the putcall parity, C = 6.5 + 42e0.04*0.5  45e0.02*0.5 =
$3.12
PROBLEM
4 Consider the same situation as in the previous . Suppose that the market price of the call option is $3. How should an arbitrager profit if
there is an arbitrage opportunity?
B. From previous, the call is underpriced. To arbitrage, buy call, short stock, and sell put. PROBLEM 5 The price of a stock is
$42 and the annual continuously compounded interest rate is 2%. The stock pays a dividend of $2 in 2 months. The European call option of strike price $45 and 3
months to expiration is sold at $0.25. What is the noarbitrage price of the European put option with the same strike price and time to expiration? B. By putcall
parity, P = 0.25 – (42 – 2e0.02*2/12) + 45e0.02*3/12 = $5.02.
PROBLEM
6 Consider an American call option. Which of the following makes the option less
valuable?
C. decreasing maturity always leads to lower prices for American options.
PROBLEM
7 The premium of a 1year 35strike call is $3.50 and the
premium of a 1year 37.50strike call is $3.75. How should an arbitrager profit if there is an arbitrage opportunity? C. Creating a bull spread will lock in a profit
of at least $0.25 in present value terms.
PROBLEM 8 Suppose the premium of a 1year 80strike call is $15 and the premium of a 1year 90 strike call is
$4.75. How should an arbitrager profit if there is an arbitrage opportunity? D. Creating a bear spread w
ill lock in a profit of at least $0.25 in present value
terms.
PROBLEM
9 Consider the same situation as in the previous. Assuming zero interest rate, what is the minimum profit that the arbitrage strategy can
generate at expiration? B. If the stock price is greater than 90, both calls are exercised. Profit = (154.75)(S80)+(S90) = 0.25.
PROBLEM
10 The prices of
three 1year call options are Strike Call 14.45 10.85 7 . 50 55 60 How should an arbitrager profit if there is an arbitrage opportunity?
A. (C(55) – C(60))/(K3 –
K2) = (10.85  7)/(60 – 55) = 0.77. (C(50) – P(55))/(K2 – K1) = (14.45 –10.85)/(55 – 50) = 0.72. So inequality (9.17) is violated. Creating a butterfly spread will
lock in a profit of at least 10.85*2(14.45+7) = 0.25 in present value terms.
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 Fall '11
 Mr.Yan
 Exchange Rate, Interest, Interest Rate

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