Part A (5 marks): When valuing European Vanilla Options in the Black-Scholes-Merton Model, there is one source of uncertainty. What is this

Part A (5 marks):

1. When valuing European Vanilla Options in the Black-Scholes-Merton Model, there is one source of uncertainty. What is this uncertainty? (3 marks)
2. Why does a short put position in a European vanilla option have positive delta? (2 mark)

Part B (5 marks):

The current price of an asset is $80, 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 Call option with strike price of $90?'

Part C (5 marks)

Two companies have investments which pay the following rates of interest: 

Firm A: Fixed - 6%, Floating - LIBOR

Firm B: Fixed - 8%, Floating - LIBOR + 1%

Assume A prefers a fixed rate and B prefers a floating rate. Show how these two firms can both benefit by entering into a swap agreement. 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? Draw swap diagram and explain.