Binomial Interest Rate Tree

Binomial Interest-Rate

Question: Finding out the one-year's forward rates for year 1 using the two-ye

r1,L Sigma

Assumption 4.07% Given 10%

Market value today PV today (Vh+C)/(1+r) (Vl+C)/(1+r)

100 100 99.59 100.41 MV= N C= r0=

V= NH C= r1,H=

99.07 4 4.976%

V= NL C= r1,L=

99.93 4 4.074%

100 0 3.50%

l Interest-Rate Tree for 2 years

using the two-year 4% on-the-run

V= NHH C= r2,HL=

V= NHL C= r2,HL=

V= NLL C= r2,LL=

V= NHHH C= r3,HHH=

0.000%

V= NHHL C= r3,HHL=

0.000%

V= NHLL C= r3,HLL=

0.000%

100 4 0.000%

100 4 0.000%

100 4 V= NLLL C= r3,LLL=

Binomial Interest-Rate T

Question: Finding out the one-year's forward rates for year 2 using the three-yea

r1,L Sigma Face Value Coupon rate Observed market price

PV today (Vh+C)/(1+r) (Vl+C)/(1+r)

Assumption 4.07% Given 10% 100 4.50% 100

MV= C= 100 r0= 99.11 100.89 N

Given

V= NH C= r1,H=

98.07 4.5 4.976%

Given

V= NL C= r1,L=

99.93 4.5 4.074%

99.57 0 3.50%

l Interest-Rate Tree for 3 years

using the three-year 4.5% on-the-run issue

V= NHH C= r2,HL=

V= NHL C= r2,HL=

V= NLL C= r2,LL=

V= NHHH C= r3,HHH=

4.5 0.000%

V= NHHL C= r3,HHL=

4.5 0.000%

V= NHLL C= r3,HLL=

4.5 0.000%

100 4.5 0.000%

100 4.5 0.000%

100 4.5 V= NLLL C= r3,LLL=

4.5