A stock index with a dividend yield of 2.2 per annum with continuous compounding is currently standing at 1200.6 and has a volatility of 20 per annum. The riskOfree interest rate is 3.5 per annum with continuous compounding. Use a fourOstep binomial tree to calculate the price of
(a) a six month long forward contract on the index, with delivery price of 1200. Calculate the theoretical value of the forward contract. Compare and comment.
(b) a European six- month CALL option with a strike of 1200. Calculate also the value of the option by using the BlackOScholes formula. Compare and comment.
(c) an American six- month CALL option with a strike of 1200.
(d) a down and out barrier CALL option with a strike of 1200 and knockout barrier of 1150 maturing in 6 months. A downOandOout call option gives the holder the right to buy the underlying asset at the strike price on the expiration date so long as the price of that asset did not go below a pre-determined barrier during the option's lifetime. When the price of the underlying asset falls below the barrier, the option is "knockedOout" and no longer carries any value.