1. If the spot price of an underlying is $50 and its volatility is 20%. Interest rates are at 10% with continuous compounding. What is the fair price for a three month call option with a strike price of $52. Show and explain your calculations.
2. XYZ and ABC enter a three year Plain Vanilla Interest rate Swap. XYZ is paying 5% fixed with semi annual compounding and receiving floating. The notional is $100 million. There are semi annual cashflows.

If the realized libor rates are:

Period 1 4.2% Period 2 4.8% Period 3 5.3% Period 4 5.5% Period 5 5.6% Period 6 5.9%

Draw a table showing the cashflows exchanged between ABC and XYZ

3)a) Use a 2 step binomial tree to value a new exotic derivative. Draw the tree and label the stock prices and derivative values at each node.

The option expires in 6 months. The interest rate is 10% annually continuously compounded. The Strike Price (K) is 100.

The spot price is at 100. U= 1.2 and D= 0.8 for each quarterly period. The payoff of this derivative is (ST/K). By this I mean that the payoff is the price of the underlying stock divided by the Strike Price.