# 15. You are working on an option trading desk in charge of arbitrage trading. The following data is

15. You are working on an option trading desk in charge of arbitrage
trading. The following data is presented to you on screen, and you immediately
see an arbitrage. What is it, and how much money can you make risk-free?

S = 60 K = 60 r =
3% T = 0:25 D = 0 CE = 5 PE = 3

16.
Stock DEF is trading at \$100 and is expected to pay a dividend of
\$3 in three months. The European call at strike 95 with half-year maturity is
priced at \$7. If the at term structure of interest rates is 5% nd a lower bound
on the price of the American put option.

17. Stock CBA is trading at price \$50 and is not expected to pay any
dividends. The following puts are traded at maturity in three months :

P (K = 50) = 5

P (K = 60) = 13

The three-month interest rate is 2%. What is
the price of a (50,60) bullish call spread?

Sundaram
& Das: Derivatives – Problems and Solutions . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . 131

18. Stock KLM trades at \$100 and pays no dividends. The one-year
straddle struck at \$102 is trading at a price of \$10. The one-year interest
rate is 2%. Find the price of the one-year European call and put.

.

19.
An investor buys a call on ABC stock with a strike price of K and
writes a put with the same strike price and maturity. Assuming the options are
European and that there are no dividends expected during the life of the
underlying, how much should such a portfolio cost?

20. Use put-call parity to show that the cost of a butter y spread
created using European puts is identical to the cost of a butter y spread using
European calls.

20. A stock is trading at S = 50. There are one-month European calls
and puts on the stock with a strike of 50. The call is trading at a price of CE = 3. Assume that the one-month
rate of interest (annualized) is 2% and that no dividends are expected on the
stock over the next month.

(a)
What should be the arbitrage-free price of the put?

(b) Suppose the put is trading at a price of PE = 2:70. Are there any arbitrage
opportunities?

22 A stock is trading at S = 60. There are one-month American calls
and puts on the stock with a strike of 60. The call costs 2.50 while the put
costs 1.90. No dividends are expected on the stock during the options’ lives.
If the one-month rate of interest (annualized) is 3%, show that there is an
arbitrage opportunity available and explain how to take advantage of it.

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