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All sub-questions a) - g) relate to the following information:

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.

This question (parts a - g) is worth 14 marks in total.

For each part, if you enter the correct answer you will receive full marks (even if you don't show working). If you choose to show working (either typed into the space provided or as one handwritten PDF file in Question 66), and get the answer incorrect, you may receive part marks. If you simply enter the incorrect answer and do not show working, you will not receive any part marks.

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? (2 marks)

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. (3 marks)

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.

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