Advanced Corporate Finance (Week 2, Swaps)

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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.

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### 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.
• A simple swap contract can be analyzed as two different bonds.
• Swap contracts (if default-free) can also be related to a package of forward contracts.
Example

Firm A and firm B are offered the following terms:

Fixed Floating

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%

• In general, if the credit spreads are not the same, there are potential swap opportunities.
• Assume Firm A prefers a floating loan and Firm B wants a fixed loan, and note that

R(b)-R(a) > r(b)-r(a).

B. VALUATION OF INTEREST-RATE SWAPS

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)

Cash flows of a swap with n periods remaining life:

t(1)

t(2)

t(3)

t(n)

(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,

Example

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?

so that

The floating-rate payer has lost \$4.27 million in this swap.

C. CURRENCY SWAPS
• Agreement to exchange both the principal and interest payments an a loan in one currency with that of another currency.
• We focus on fixed-rate loans only.
• Example: Firm A and firm B are offered the following fixed-rate terms

Assume Firm A wants to borrow sterling and firm B wants to

borrow dollars.

D. VALUATION OF CURRENCY SWAPS

where S is the exchange rate.

Example: See Hull’s book.

E. ISSUES AND FACTS CONCERNING SWAPS
• Quality spreads tend to increase with loan maturity.
• Low credit-worthy party tends to prefer fixed rate loans.
• Credit spread differential persists over time and “credit arbitrage”do not eliminate these differentials.
• There are default and market riskes involved in swaps.
• The potential ‘systematic risk” of swaps, i.e., the chain-effects upon default of a party, is still not well understood.