Question

Exercise 7.3. There are three assets in the economy, stock, money, and call option. The stock price tomorrow can be either 5 or 15 depending on the economy's performance. The money price tomorrow is 1 independent of the economy's performance. The call option has a strike price of 10 (if you oun one unit of the call option, you are entitled to purchase a share of stock tomorrow at the strike price). Suppose today's prices for a share of stock is 12, for money is 1, and for an unit of the call option is 4. Question: Is there an arbitrage (A portfolio that has a negative price today and non- negative value in all circumstances tomorrow)? If an arbitrage exists, please find one there may be many). If no arbitrage erists, explain why.

Answer 1

ANSWERS let us assume wealth of $1,200, the investor can buy 100 shares od 300 Call options (120019 Investor's poor Good strategy Economy Economy Buy 100 -700 Shares 300 13,800 Buy 2o cau 200 option contracts - Maximum loss the investor incurs by holding out the options is the cost of the controuct is: - $ 1200 - (4x $300) > maximum gain the investor incuss by holding out options QS =(1540 x 3000-1200 = 5x3000-1200 = 15,000-1200 $13,800 > Hence, ?t YS very clear that there as an aurbitage oppustunity if he holds onto the option controuct.