FIN672: Financial Instruments and derivaties.

Explain your answer, and show your work if required as well as any sources used.
1. Intuitively speaking, how does the delta of a deep OTM call change as volatility increases?
2. You hold a portfolio that is short 2,000 puts, each with a delta of -0.63. What would you do to delta-hedge the portfolio?
3. A stock is currently trading at $22.50. The delta of an at-the-money call on the stock is 0:56 and the gamma is 0.035. If the stock price were to change to $22.25, by how much would the call price change (using the delta alone)? What is the approximate new value of the call delta?
4. What is the relationship of a swap to fixed- and floating-rate bonds?
5. What is the impact on the value of a swap if, ceteris paribus, the volatility of interest rates rises?
6. Firm A can borrow fixed rate at 10%. It can also borrow floating at Libor 1%. The market swap rate at the bid is Libor versus 8.9% and is Libor versus 9.1% at the ask (i.e., the firm can enter into a swap by paying fixed at 9.1% or receiving at 8.9%). Find the cheapest form of financing for the firm if it wishes to be in floating-rate debt. We already know that the firm can borrow at Libor 1%. We need to check if it can do better by borrowing fixed and then swapping into floating. So compare these 2 alternatives.