Question:
At time zero you enter a long position in a forward contract on 8 shares of the stock XYZ at the forward price of $60.00. Moreover, you sell (write) 10 exotic options each of which gives the holder one share of the stock (only) if the price of one share is above $55.00 and which pays the holder $50.00 (only) if the price is below $55.00. The today's selling price of one option of this kind is $53.00. You also buy 2 zero-coupon bonds with continuously compounded annual yield of 5%, with face value of $100.00 each. The maturity of all of your positions is T = 3 months. What is your total profit or loss if
a. at maturity the price of one stock share is $58.00?
b. at maturity the price of one stock share is $47.00?
You may assume that the initial wealth is not invested/borrowed, that is, it grows at zero interest rate.