In the Black Scholes and Merton framework we can form an "instantaneously riskless" portfolio of one short option plus "delta" times the current spot price of a stock: (S₀).

For example: if the delta of a short option is 0.4, an instantaneously riskless portfolio can be created by buying 0.4S₀ .

A.Explain why is this portfolio is considered instantaneously riskless? Your answer should include a definition of what "risk" is being hedged in the portfolio

B.What will happen to the riskless portfolio if the stock price changes?

The current price of a non-dividend paying asset is $45 and the current riskless interest rate is 5% p.a. continuously compounded. What would be the lower boundary for a European call option written on the asset which has a strike of $50 and a time to maturity of 2 years? Please show all working.

Two firms have currently have loans for which they must pay the following rates of interest:

Fixed Float

Firm A 7.5% Libor

Firm B 8.8% Libor+0.3%

Assume A prefers a floating rate of interest and B prefers a fixed rate of interest.

If an intermediary charges both parties a 0.3% fee each, and any benefits are spread equally between Firm A and Firm B, what rates could A and B receive on their preferred interest rate? Please show all working. You do not need a diagram to answer this question.