Question

A 2-year deferred interest rate swap with decreasing notional amounts and a 4 year term is priced based on the data in the table below. Calculate the swap rate Zero Coupon Bond Price Notional Amount 1 Year Forward Rate(maturity Spot Rate erm (n) in ars 4 million 3 million 2 million 1 million 3.5% 4.5% 5.5% 6.0% 3.500% 5.510% 7.529% 7.514% value 100 96.62 91.57 85.16 79.21 2 4 A.) 7.28% B.) 7.41% C.) 7.52% D.) 7.65% E.) 7.78%

Answer 1

The correct answer is option C) 7.52%

Please note that this is a deferred swap with changing notional amount.

The fixed swap rate is changing notional principal times price of a zero coupon bond, weighted average of implied forward rates. If the text is confusing, please see the formula below:

-Σ-k Qt, P(0.ti) F(ti-l , t.)

where

R = Fixed rate of the swap

k = period when swap starts, in our case it's 2 year deferred swap. So, the swap starts from k = 3

n = 4

Q_ti = Notional for the period i

P(0, t_i) = Price of a zero coupon bond with maturity at t_i for a maturity value of $ 1

F(t_i-1, t_i) = Forward rate between period t_i-1 and t_i

Please see the table below now:

• Columns highlighted in yellow are those that we have to calculate to solve this problem
• Other columns are the ones already given in column
• Please see the second row. That will guide you how each of the columns have been calculated.
• You can now locate the variables Q, P & F in the columnar form (please see second row)

Term	Notional Amount	Spot Rate	1 year forward rate	Zero coupon bond price (maturity value = $ 100)	Zero coupon bond price (maturity value = $ 1)
i	Q	A	F	B	P = B / 100	C = Q x P x F	D = Q x P
1	4	3.50%	3.500%	96.62	0.9662
2	3	4.50%	5.510%	91.57	0.9157
3	2	5.50%	7.529%	85.16	0.8516	0.128233928	1.7032
4	1	6%	7.514%	79.12	0.7912	0.059450768	0.7912

R = (0.128233928 + 0.059450768) / (1.7032 + 0.7912) = 0.187684696 / 2.4944 = 0.075242421 = 7.52%

Hence, the correct answer is option C) 7.52%