Part A: i. When valuing European Vanilla Options in the Black-Scholes-Merton Model, there is one source of uncertainty. What is this uncertainty? (3 marks) Max 50 words. ii. Why does a short call position in a European vanilla option typically have negative delta (Δ)?

Part B. The current price of a non-dividend paying asset is $65, the riskless interest rate is 5% p.a. continuously compounded, and the option maturity is five years. What is the lower boundary for the value of a European vanilla put option on this asset with strike price of $80?

Part C. Two companies have investments which pay the following rates of interest: Fixed Float Firm A 6% Libor Firm B 8% Libor + 0.5% Assume A prefers a fixed rate and B prefers a floating rate. If an intermediary charges both parties equally a 0.1% fee and any benefits are spread equally between Firm A and Firm B. If an intermediary charges both parties equally a 0.1% fee and any benefits are spread equally between Firm A and Firm B, what rates could A and B receive on their preferred interest rate? Show all working.