INTEREST RATE SWAPS: INTEREST RATE SWAPS Professor Kian-Guan Lim
Singapore Management University SWAPS: SWAPS Definition
A swap is an agreement between two or more parties to exchange sets of cash flows over a period in the future.
Example: a fixed interest rate is swapped for a floating interest rate
The parties that agree to the swap.
Basic Kinds of Swaps
interest rate swaps and currency swaps PLAIN VANILLA SWAPS: PLAIN VANILLA SWAPS Example I: A Plain Vanilla Interest Rate Swap
Assume the swap covers a 5-year period and involves annual payments on a $1m principal amount.
Notional Principal: $1m
plays a notional role in determining the amount of interest payment, but is not actually transferred.
is the difference between the two obligations that actually takes place PLAIN VANILLA SWAPS (continued): PLAIN VANILLA SWAPS (continued) Example II: A Plain Vanilla Currency Swap of 10M USD
Assume: the current spot FX rate is 1.5 S$ per USD U.S. interest rate = 5%; S$ interest rate = 4%
Initial cash flow:
Annual int. payment:
Repayment of Principal: Party C Party D Party C Party D S$ 600,000 USD 500,000 S$ 15 m USD 10m MOTIVATIONS FOR SWAPS: MOTIVATIONS FOR SWAPS Commercial Needs
to change the characteristics of the borrowing to one that meets the firm’s specific needs.
A savings and loan association with floating rate liabilities and fixed rate assets is facing the risk of rising interest rate.
it wishes to transform a fixed rate mortgage asset into an asset that pays a floating rate of interest. MOTIVATIONS FOR SWAPS (continued): MOTIVATIONS FOR SWAPS (continued) Motivation for the Plain Vanilla Interest Rate Swap borrower MOTIVATIONS FOR SWAPS (continued): MOTIVATIONS FOR SWAPS (continued) Comparative Advantage
Firms can use swaps to borrow in the cheapest form.
Two firms enjoy comparative advantages in borrowing Dollars and Euros respectively.
Table I. Borrowing Rates for Two Firms in Two Currencies
+1 +2 C has absolute advantage in both currencies, but relatively more advantage in borrowing Euro (2% cheaper) than in borrowing USD (1% cheaper) compared to D MOTIVATIONS FOR SWAPS (continued): MOTIVATIONS FOR SWAPS (continued) Motivation for the Plain Vanilla Currency Swap
Spot exchange rate EURUSD 1.3
Exchange of Borrowings Party C Party D Euro 10 m USD 13 m Lender Lender Euro 10 m USD 13 m Pays 6.5% interest Pays 5% interest SWAP FACILITATORS: SWAP FACILITATORS Definition
A swap facilitator is a third party who assists in the
completion of a swap.
Types of Facilitators
More on Swap Dealers
it fulfills all of the functions of a swap broker
it may take risk by becoming a counterparty in the swap
it seeks to minimize that risk by forming a swap with another counterparty.
SWAP FACILITATORS (continued): SWAP FACILITATORS (continued) An Example on the Role Played by a Swap Dealer
Assume the dealer begins with its optimal set of investments, then it enters the following transactions (notional $1m):
Table II. The Swap Dealer’s Net Cash Flows
Party E Fixed: 12% Floating: LIBOR +3.1% 5 yrs 3 yrs exposure PRICING OF SWAPS: PRICING OF SWAPS Factors that Affect Swap Pricing
Creditworthiness of the counterparties
there is no clearinghouse in the swaps market.
The default risk is assumed by the dealer.
A swap default has less risk than a bond default under the net payment
the dealer adjusts the pricing to reflect the default risk.
Availability of additional counterparties
The dealer seeks other counterparties to offset the risk involved in a prospective swap.
The term structure of interest rates
pricing of interest rate swaps must reflect the prevailing term structure in the bond market to avoid arbitrage.
PRICING OF SWAPS (continued): PRICING OF SWAPS (continued) The Indication Swap Pricing Schedule
Table III. Sample Swap Indication Pricing
Bid-ask basis points added to Reference T-Note yield 8.14% swapping for LIBOR PRICING OF SWAPS(continued): PRICING OF SWAPS(continued) Example: An interest rate swap of 7 years
Assume: the swap bank’s customer pays LIBOR flat
Assume: the swap bank’s customer pays a fixed rate Customer Bank Floating: LIBOR Fixed: 8.14% + 0.82% Customer Bank Fixed: 8.14% + 1.02% Floating: LIBOR SWAP PORTFOLIOS: SWAP PORTFOLIOS Risks in Managing a Swap Portfolio
Default risks of the dealer’s counterparties
Basis risk: the risk that normal relationship between two prices may change (basis swap)
e.g. in Scenario II, the market disturbance in Europe may change the normal relationship between LIBOR and the T-note rate. As a result, the bank suffers a loss by paying a higher LIBOR than it initially anticipated.
Mis-match risk: the risk occurs when the dealer cannot offset its entire risk through another swap, and has exposures
Interest rate risk (e.g. fixed to floating swap) SWAP PORTFOLIOS(continued): SWAP PORTFOLIOS(continued) Managing Mis-match and Interest Rate Risk
by participating in other swaps
by participating in the futures market
e.g. In Table II, the dealer faces both mis-match and interest rate risk in year 4 & 5. It can offset the risk either by arranging a third swap in which it pays the fixed rate and receives the floating rate, or it can sell Eurodollar futures with a distant expiration since Eurodollar futures price will fall with rise in LIBOR.
BEYOND THE PLAIN VANILLA: BEYOND THE PLAIN VANILLA Flavored Interest Rate Swaps
The characteristics of the notional principal or the payments derived from that principal are altered to go beyond the plain vanilla swaps.
Amortizing Swap (notional principal decreases over time)
Accreting Swap (notional principal increases over time)
Seasonal Swap (notional principal varies over time by schedule)
Roller Coaster Swap (mix of accreting and amortizing swaps or also switches in payer and receiver swaps)
Off-Market Swap (fixed payer pays above market rate but receives a present cash receipt of PV of excess payment)
Basis Swap (floating to floating based on different indexes)
Yield Curve Swap (floating to floating based on indexes of different tenors)
Quanto or differential/diff swap (floating currency X to floating currency Y interest rates on same currency X notional) BEYOND THE PLAIN VANILLA: BEYOND THE PLAIN VANILLA Flavored Currency Swaps
Seasonal currency swap (varied notional principal)
Fixed-for-fixed currency swap
Fixed-for-floating currency swap
Circus Swap (essentially fixed for fixed but 3 counterparties)
Example:A pair of fixed-for-floating currency swaps = a circus swap
Fixed Euro OTHER TYPES OF SWAPS: OTHER TYPES OF SWAPS Commodity Swaps
there is an underlying notional principal
specified as amount of a commodity in the commodity swaps
specified as a stock portfolio in the equity swaps
there is a fixed tenor
one party pays a fixed rate while the other pays a floating rate.
e.g. fixed price for gold swapped for current price
e.g. S&P 500 return swapped for fixed percentage return OTHER TYPES OF SWAPS: OTHER TYPES OF SWAPS Forward and Extension Swaps
a forward swap: counterparties agree that the cash flows will begin at a date in the future.
An extension swap: counterparties agree to the extension of an existing swap.
a swaption is an option on a swap
the buyer of a call swaption pays a premium for the option and by maturity has the right to buy a swap at the fixed rate (exercise price). He/she pays the fixed rate and receives the floating rate in an interest rate swap.
The seller of a call swaption is obligated to engage in the exercised swap by receiving fixed and paying floating.
SWAPTION (continued): SWAPTION (continued) An example of a European Call Swaption
Assume the underlying swap is a five-year swap with annual payments and a notional principal of $ 10m. If exercised, the buyer of the call swaption pays a fixed rate of 8% and receives a floating rate of LIBOR+50 basis points.
The premium of the swaption is stated as 30 basis points on the notional principal.
The buyer (exercise into a fixed payor swap) will exercise the swaption if the fixed market rate for a fixed-floating LIBOR swap is above the 7.5% at the time of expiration of the call.
Important terms: Important terms To buy a swap means to buy a fixed payor swap or to pay fixed and receive floating
To sell a swap means the reverse, to pay floating and receive fixed
To buy a call swaption means to buy the right to exercise into a long swap :- pay fixed receive floating
To buy a put swaption means to buy the right to exercise into a short swap :- pay floating receive fixed
AN INTEREST RATE SWAP AS A PORTFOLIO OF FORWARD CONTRACTS: AN INTEREST RATE SWAP AS A PORTFOLIO OF FORWARD CONTRACTS An example of a forward contract:
Buy forward today: Dec 15, 06; maturity date: Dec 15, 07
- The underlying asset: $ 1m face value of 3-month Eurodollar deposits at a yield of 9%.
- The contract essentially establishes a fixed rate 9% payment on the $ 1m face value.
The purchaser of the forward contract (“lends” at fixed 9% for 3 months at maturity) gains when the market yield at the expiration date is lower than 9%, say 8%.
The purchaser receives fixed 9% and pays floating.
- Cash settlement of forward: $gain = (9-8)% x $1m x 0.25
In essence, an interest rate swap can be analysed as a portfolio of forward contracts with successive expiration dates.
Similarly, it can be considered as a strip of interest rate futures contracts. CREATING SYNTHETIC SECURITIES WITH SWAPS: CREATING SYNTHETIC SECURITIES WITH SWAPS Synthetic Fixed Rate Debt (floating rate loan + swap)
Synthetic Floating Rate Debt (fixed rate loan + swap)
Swap: receive floating pay fixed Pay fixed Swap: receive fixed pay floating CREATING SYNTHETIC SECURITIES WITH SWAPS: Synthetic Callable Debt
combining a non-callable debt with the purchase of a put swaption, an initial debt obligation (by issuer) converts into a callable bond.
Essentially, a fixed rate payment is converted into a floating rate payment depending on the market condition.
CREATING SYNTHETIC SECURITIES WITH SWAPS Firm buys put swaption: right to exercise into receive fixed & pay floating CREATING SYNTHETIC SECURITIES WITH SWAPS: Synthetic Non-callable Debt (callable + sell put swaption)
Synthetic Dual-Currency Debt (receive $ principal, but pay Euro interest, return $ at maturity = $bond + fixed for fixed foreign currency swap) CREATING SYNTHETIC SECURITIES WITH SWAPS Firm issues callable Debt Pay fixed interest on debt Firm continues to pay fixed as if it is non-callable. The floating receipt goes toward a fresh debt as if it was not called. Firm sells put swaption: may be called to pay fixed & receive floating If firm calls debt because floating rate has dropped, the put swaption is exercised against it. PRICING INTEREST RATE SWAPS: PRICING INTEREST RATE SWAPS Slide27: In a coupon (plain vanilla) IRS, the fixed rate payer is the buyer. The buyer locks in fixed borrowing rates. The fixed rate receiver is the seller. The seller locks in fixed lending rates. The IRS buyer pays a fixed rate to the IRS seller, and in turn receives a floating rate at each reset date.
The fixed rate (swap rate or coupon rate or strike rate) is prefixed at trade date. The floating rate is prefixed at trade date to be the rate on a prefixed benchmark, e.g. LIBOR, at the start date and subsequent reset dates.
The IRS is cash-settled at the end of each period after reset, in which case it is IRS in-fine. If IRS is cash-settled at the reset date itself (usually 2 business days after reset), then it is IRS in-arrears. For in-arrears IRS, the last payment is at the last reset one period before maturity. For in-fine IRS, the last payment is one period after the last reset, i.e. at maturity. Payment is typically made a business day or two after settlement date, at payment date. Two types of Interest Rate Swaps Slide28: The sequence of payments based on the fixed swap rate is called the “fixed leg” of the swap. The sequence of payments based on the floating rate index e.g. LIBOR is called the “floating leg” of the swap.
A floating for floating interest rate swap where each floating is based on different floating rate index is called a basis swap.
LIBOR is quoted on a money market yield basis, or add-on rate, i.e. interest is added onto the notional principal.
The effective period used to compute the interest is called the accrual factor or daycount fraction. For LIBOR, the day count basis for floating payment is “actual/360”, and yields an accrual factor of t/360 as above, for settlement. For fixed payment, there are several fixed day count conventions.
IRS that originates with zero initial cost or price is called a par swap. The fixed rate for a par swap is called the par swap rate.
Swaps where start date = trade date are spot swaps, i.e. s=0. The par swap rate is called the swap rate. These swaps are the most common. Screen quotations reflect these swap rates.
Swaps where s>0 are called forward start swap. The par swap rate is called the forward swap rate. Some Common Swap Terms THREE REPRESENTATIONS OF IRS: THREE REPRESENTATIONS OF IRS THREE REPRESENTATIONS OF IRS: THREE REPRESENTATIONS OF IRS THREE REPRESENTATIONS OF IRS: THREE REPRESENTATIONS OF IRS Slide32: T is trade date. S is first reset date. Swap zero coupon (spot rate) LIBOR curve : Swap zero coupon (spot rate) LIBOR curve Slide34: Valuation of vanilla (generic fixed vs. floating) IRS Slide35: Valuation of vanilla (generic fixed vs. floating) IRS