1. A European call option has a strike price of $20 and an expiration date in six months. The premium for the call option is $5. The current stock price is $25. The risk-free rate is 2% per annum with continuous compounding.What is the payoff to the portfolio, short selling the stock, lending $19.80 and buying a call option? (Hint: fill in the table below.)

Value of S_T

Payoff

S_T 20

S_T > 20

How much do you pay for (or receive with) this portfolio at date 0? Is there an arbitrage opportunity?

If there is an arbitrage opportunity, then answer the following:

What is the minimum profit, expressed as a present value? Will investors trade to exploit the opportunity? If they will trade to exploit the opportunity, explain why security prices change and describe how security prices change.(30 points)