i) When valuing European Vanilla Options in the Black-Scholes-Merton Model, there is one source of uncertainty. What is this uncertainty? Max 50 words.

ii) Why does a short call position in a European vanilla option typically have negative delta (Δ)? Max 75 words

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:

Firm A: Fixed- 6%, Float- Libor

Firm B; Fixed- 8%, Float- 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.