Part A (5marks)

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 typically have negative delta ()?

Part B(5marks)

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(5marks)

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?

Part A (5marks) i. When valuing European Vanilla Options in the BlackScholesMerton Model, there is one source of uncertainty. What is this uncertainty? ii. Why does a short call position in a European vanilla option typically have negative delta ()? Part B (5marks) The current price of a nondividend 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 (5marks) 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