Question

# A one-month European call option on a non-dividend-paying stock is currently selling for\$2.50. The stock price...

A one-month European call option on a non-dividend-paying stock is currently selling for\$2.50. The stock price is \$47, the strike price is \$50, and the risk-free interest rate is 6% per annum. What opportunities are there for an arbitrageur?

First we will calculate the present value of strike price:

50e-0.06*1/12 = 49.75

As 2.5<49.75-47, an arbitrgeur should borrow \$49.50 at 6% for on month, buy the stock and buy the put option. This position will help in generating the profit. If the stock price goes above \$50 in one month, th option expires worthless, but the stock can be sold for atlest \$50. As the present value of \$50 is \$49.75, therefore the strategy will generate the profit of \$0.25

If the stock price goes below \$50, the put option is exercised and profit will be generated of \$0.25.

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