Question

# What are the upper and lower bounds for the price of a two-month put option on...

What are the upper and lower bounds for the price of a two-month put option on a non-dividend-paying stock when the stock price is \$27, the strike price is \$30, and the risk-free interest rate is 5% per annum? What is the arbitrage opportunity if the price of the option is \$1? What are the net profits?

max.(Ke-rT -S0 ,0)<p <Ke-rT

Lower bound:- 30*e-0.05*(2/12) - 27 = \$2.75

Upper bound: \$29.75

Since, \$1 < \$2.925,

An arbitrageur should borrow \$28 at 5% for one month, buy the stock, and buy the put option. This generates a profit in all circumstances.

If the stock price is above \$30 in one month, the option expires worthless, but the stock can be sold for at least \$30. A sum of \$30 received in one month has a present value of \$29.75 today. The strategy, therefore, generates profit with a present value of at least \$1.75

If the stock price is below \$30 in one month the put option is exercised and the stock owned is sold for exactly \$30 (or \$29.75 in present value terms). The trading strategy, therefore, generates a profit of exactly \$1.75 in present value terms.

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