(a.) Define an American option, (b.) An investor buys 5,000 units of an European call option contract at a strike price E of E3,000.00. In 12-months time, the asset price S12=E3,500.00. Find the pay-off of this contract if the premium is E350.00. (a.) Define the European option. (b.) An call option expiring in 2-years has an exercise price of E1,500.00 on the Eswatini stock market and currently trades at E1,840.00. It is anticipated that the stock will rise by a factor of 1.10 and fall by a factor of 0.80. If the interest rate is 3%; (a.) Define a portfolio in a market and give the conditions for it to be self financed. b.) A stock market trades an asset whose market price change s given by dX(t)=2X(t)dt+dB(t);B(0)=0. What is the expected price E[X(t)] and the variance 2(X(t)