Part A: 

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

ii. Why does a short call position in a European vanilla option 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 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. 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?