Advanced Corporate Finance (Week 2, Swaps). Dr. L. Zou Finance Group UvA. A. INTEREST RATE SWAPS. Interest Rate Swap: Financial agreement to exchange interest payments of a fixed-rate loan with a variable-rate loan. London Interbank Offer Rate (LIBOR) as a benchmark for the floating rate.
Dr. L. Zou
Firm A and firm B are offered the following terms:
Firm A R(a) = 10.0% r(a) = LIBOR + 0.3%
Firm B R(b) = 11.2% r(b) = LIBOR + 1.0%
Credit Spread R(b) - R(a) =1.2% r(b) - r(a) = 0.7%
R(b)-R(a) > r(b)-r(a).
Define B(1) = Value of fixed-rate loan
B(2) = Value of floating-rate loan
V = B(1) - B(2) = Value of swap
Q = Face value of loan
k = fixed-rate payment per period
= floating-rate payment for time t(i)
k* = next floating-rate payment r(i) = continuously compounded discount rate for t(i)
(1) - k
(2) - k
(3) - k
(n) - k
Following the bond pricing formula
And, nothing that a floating-rate bond will sell for its par value
if the rate is used as the discount rate,
A swap involves a 6 month LIBOR floating rate and and 8% fixed rate (semi-annual compounding). It has Q=100,000,000 and a remaining life of 1.25 years. We have t(1)=0.25, t(2)=0.75 and t(3)=1.25.
Assume that the appropriate discount rates (continuously compounded) are r(1) = 10%, r(2) = 10.5% and r(3) = 11%; and the last LIBOR = 10.2%.
What is the swap’s value?
The floating-rate payer has lost $4.27 million in this swap.
Assume Firm A wants to borrow sterling and firm B wants to
where S is the exchange rate.
Example: See Hull’s book.