A stock price is currently $100. In EACH YEAR of the next two years it is expected that the stock will have one of two outcomes: either it goes up by 20% over the coming year or goes down by 10% over the coming year (no other outcome is possible and outcomes in each year are independent).

The risk-free interest rate is 6% per annum with continuous compounding. Assume that there is no transaction cost associated with trading either the stock or the derivative, whether for long or short positions.

For sub-questions a) - d):

Assume that you are long a ONE-YEAR European call option with a strike price of $110 and you want to hedge your position in this option with the stock by creating a riskless portfolio (i.e. the value of this portfolio will not depend on whether the stock price goes up or down in 1 year's time).

For sub-questions f) - g):

Assume that you are long a TWO-YEAR European call option with a strike price of $110.

f) Now, assume that you are long a TWO- YEAR European call option with a strike price of $110.

What are the 4 possible payoffs on this call option at the end of year 2?

g) As for part f), assume that you are long a TWO- YEAR European call option with a strike price of $110.

Use risk-neutral probability to calculate the price of this two-year European call option today.

Enter your answer to 2 decimal places eg if your answer is 5.547 enter as 5.55, if your answer is 5.503 enter as 5.50.