Vlad Tepes, Prince-Protector of Wallachia temporarily purchases (or loans), for a term of 5 years, the rights to use the income of the lands of Tirgoviste, which is worth 1,000,000 ducats. At the end of every year, there will be an interest payment with respect to the floating rate available at the beginning of that year. At the end of the term, the lands are returned (similar to capital return). The term structure at the time is as follows:

r_k = 0.08 + 0.02k, for k = 1, 2, 3, 4, 5.

However, as Wallachia has a relatively small economy, Vlad wants no risk and asks Mehmed II, of Ottoman Empire to act as a financial guarantor who ensures Vlad's total cash outflow at each payment period is based on some fixed payments based on a con- stant swap rate. (Vlad is the Dracula.)

(a) (5 points) Assuming the land value of Tirgoviste stays constant throughout the term, what would be the swap rate corresponding to this agreement.

b) (5 points) Assume Tirgoviste is worth 1,000,000 through the first three years, im- mediately after which, due to great prosperity in this region, is envisioned to increase to 2,000,000. In the remaining portion of the term this value stays fixed. Find the new appropriate swap rate under this new forecast.

c) (5 points) Suppose the at the end of the second year we have a new term structure:

r_k*= 0.1 +0.04k, for k = 1,2,3, 4.

Find the market value (at time 2) of this swap assuming the scenario in part (b) still holds true. Who has the right to sell the swap agreement: Vlad or Mehmed?