A stock market investor has $500 to spend and is considering purchasing 10 call option contracts on 1,000 shares of Banana Computer stock.

The shares themselves are currently selling for $28.50 per share.

Banana is involved in a lawsuit, the outcome of which will be know within a month. If the outcome is in Banana's favor, analysts expect Banana's stock price to increase by $5 per share. If the outcome is unfavorable, then the price is expected to drop by $2.75 per share. The 10 call option contracts with a strike price of $30 per share and an expiration date in one month cost $500 right now.

Besides purchasing the call options, the investor could :

(i) do nothing and earn 8% per year compounded monthly on $500

(ii) purchase 17 shares of Banana stock right now and earn 8% per year compounded monthly on the rest of the money

Suppose the probability that Banana wins the lawsuit is p, 0 < p < 1 .

Assuming that the investor is risk-averse and his/her risk attitude is described by the exponential utiloty function U(x)=1-e^(-x/R), where R is the risk tolerance, R=2,500.

What are the values of p that will make the investor choose to do nothing?

What are the values of p that will make the investor choose to buy shares of Banana stock?

What are the values of p that will make the invesstor choose to buy call options?