question archive building an n =10-period binomial model for the short-rate, ri,j
building an n =10-period binomial model for the short-rate, ri,j
Subject:FinancePrice: Bought3
building an n =10-period binomial model for the short-rate, ri,j . The lattice parameters are: r0,0 = 5%, u = 1.1, d = 0.9 and q =1 - q = 1/2.
1) Compute the initial value of a forward- starting swap that begins at t = 1 , with maturity t = 10 ,& a fixed rate of 4.5%(The first payment that takes place at t = 2 and the final payment takes place at t = 11 as we are assuming, as usual, that payments take place in arrears. You should assume a swap notional of 1 million, and assume that you receive floating and pay fixed.)
2) Compute the initial price of a swaption that matures at time t = 5 and has a strike of 0 . The underlying swap is the same swap as described in the previous question with a notional of 1 million. To be clear, you should assume that if the swaption is exercised at t = 5 then the owner of the swaption will receive all cash-flows from the underlying swap from times t = 6 to t = 11 inclusive. (The swaption strike of 0 should also not be confused with the fixed rate of 4.5% on the underlying swap.)
