Q1 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.
a) What is the total gain for each strategy if the stock price at maturity is
$115?
b) What is the total loss if the stock price is $92 at maturity?
c) How high does the stock price have to rise for the option strategy to be
more profitable?
d) Draw a diagram showing how the profits of these two alternative strategies
depends on the stock price in 3 months.
e) What advice would you give to this investor?


Q5 Suppose that 3-month, 6-month, 12-month, and 2-year OIS rates are 4.0%,
4.8%, 5.5%, and 6.4%, respectively. The 3-month, 6-month and 12-month
OISs involve a single exchange at maturity; the 2-year OISs involve quarterly
exchanges. The compounding frequencies used for expressing the rates correspond to the frequency of exchanges.
a) Calculate the OIS zero rates using continuous compounding. Interpolate
linearly between continuously compounded rates to determine rates between 6 months and 12 months, and between 12 months and 2 years. (Use
your calculator to find 3-month, 6-month, 12-month OIS rates. Use Excel
to find 2-year OIS rate.)
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b) What are the forward rates for the periods: 6 months to 12 months, 12
months to 24 months?
c) What is two-year par yield? Assume coupons are paid twice in a year.
d) Suppose the risk-free rates are as you calculated in a). If we know the current forward LIBOR rate for the six-month period beginning in 6 months
is 6.7% (semiannually compounded), what is the value of an FRA where
the holder pays 6.5% (semiannually compounded) for that six-month period in 6 months? The principal is $100 million.


Q6 Consider a dividend-paying stock. The spot price in April is $50. Dividends of
$0.75 per share are expected in July and October. An investor wants to short
1,000 shares and purchase them back in November. Show the cash flows of this
investor’s transactions if the price in November is $48. Will she gain or loss by
shorting? (Suppose the risk-free interest rate is 0.)


Q7 Consider a 2-month forward contract on a non-dividend paying stock with a
current price of $60. The risk-free interest rate continuously compounded is
6.5% p.a.
a) What should be the theoretical forward price?
b) If the forward price is $60.95, use a cash flow table that is similar to what
we learned in class to show how you would arbitrage from this forward
price.
c) If the forward price is $60.35, use a cash flow table that is similar to what
we learned in class to show how you would arbitrage from this forward
price.