Compute the initial price of a swaption that matures at timet = 5

t=5and 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 att = 5

t=5then the owner of the swaption will receive all cash-flows from the underlying swap from timest = 6

t=6tot = 11

t=11inclusive. (The swaption strike of 0 should also not be confused with the fixed rate of 4.5% on the underlying swap.)

should be answered by building ann =

n=10-period binomial model for the short-rate,r_{i,j}

ri,j

. The lattice parameters are:r_{0,0} = 5\%

r0,0

=5%,u = 1.1

u=1.1,d = 0.9

d=0.9andq =1-q = 1/2

q=1q=1/2.