We are trading shares at t=0 with Stock Price P= 100 . Company that issues the shares declares they will NOT pay dividends.

The share price is dependent on Country A Economy's performance. If performance is great, then share price goes UP by 40%. BUT if it is bad it goes DOWN by 11% with equal probabilities. The risk-free rate is 4%.

This product is an Asian exotic option with exercise taking place at t=1 but the person who exercises it with STRIKE PRICE K= $ 100, pays the STRIKE price and receives the payoff/ profit back in the next year t=2.

The payoff structure across the 3 years (now t=0, t=1 and t=2 ) is given by max function: max (P0, P1, P2).

In the case that it is not exercised at t=1, then the person who owns it does not gain any profit at t=2 .

Question 1:

Calculate the price of the option when the stock price is P1= 140 at t=1.

Question 2:

Calculate the price of the option when the stock price is P1= 89 at t=1.

Question 3:

What is the price of the option in the beginning at t=0 ?

Question 4:

If we wish to create portfolio at t=0 which includes shares and bonds (principal= $100) that mimics the payoffs of the option at t=1 , then what composition of shares and bonds should there be?

Question 5:

How much return should we expect for this particular option at t=0 and t=1 ?