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6.5 The swap rate curve:

6.5.1 Its use in Valuation by market participants

  • Interest rate swaps are derivative contracts, where one party exchanges fixed-rate interest payments for floating-rate interest payments with another party. The Swap rate: is the interest rate for the fixed-rate leg of an interest rate swap.
  • The yield curve of swap rates is called the 'swap curve'
  • The swap curve is based on so-called par swaps, in which the fixed rates are set so that no money is exchanged at contract initiation-the present values of the fixed-rate and benchmark floating-rate legs being equal. The swap curve is a type of par curve.
  • The level of the swap rate is such that the swap has zero value at the initiation of the sap agreement Floating rate: are based on some short-term reference interest rate
  • Examples of floating reference rates are three-month or six-month dollar Libor (London Interbank Offered Rate), euro-denominated Euribor (European Interbank Offered Rate), and yen-denominated Tibor (Tokyo Interbank Offered Rate). The swap rate curve (versus the government spot curve) might be used in fixed-income valuation depending on the business operations of the institution using the benchmark.
  • For example, wholesale banks frequently use the swap curve to value assets and liabilities because these organizations hedge many items on their balance sheets with swaps.

Swap contracts are non-standardized and are simply customized contracts between two parties in the over-the-counter market.

  • The fixed payment can be specified by an amortization schedule or be coupon paying with non-standardized coupon payment dates.
  • To price a swap, we need to determine the present value of cash flows for each leg of the transaction.
  • In an interest rate swap, the fixed leg is fairly straightforward because the cash flows are specified by the coupon rate set at the time of the agreement.
  • Pricing the floating leg is more complex because, by definition, the cash flows change with future changes in interest rates.
  • The forward rate for each floating payment date is calculated by using the forward curves.

6.5.2 Determination and Interpretation of the swap Spread for a default-free bond

The swap spread is defined as the spread paid by the fixed-rate payer of an interest rate swap over the rate of the 'on-the-run' government security with the same maturity as the swap.

  • Often, fixed-income prices will be quoted in SWAPS +, for which the yield is simply the yield on an equal-maturity government bond plus the swap spread
  • For euro-denominated swaps, the government yield used as a benchmark is most frequently bunds (German government bonds) with the same maturity. Gilts (UK government bonds) are used as a benchmark in the United Kingdom.

Example. If the fixed rate of a five-year fixed-for-float Libor swap is 2.00% and the five- year Treasury is yielding 1.70%, the swap spread is 2.00% – 1.70% = 0.30%, or 30 bps.

A Libor/swap curve is probably the most widely used interest rate curve because it is often viewed as reflecting the default risk of private entities at a rating of about A1/A+, roughly the equivalent of most commercial banks.

The swap spread helps an investor to identify:

  • Time value
  • Credit
  • Liquidity components of a bond's yield-to-maturity
  • The term "swap spread" is sometimes also used as a reference to a bond's basis point spread over the interest rate swap curve and is a measure of the credit and/or liquidity risk of a bond.
  • If a bond is default-free, then the swap spread could provide an indication of the bond's liquidity or it could provide evidence of market mispricing.

6.5.3 Z-SPREAD

Zero-spread (Z-Spread) – A more accurate measure of credit and liquidity than swap spreads.

The Z-spread is the constant basis point spread that would need to be added to the implied spot yield curve so that the discounted cash flows of a bond are equal to its current market price.

This spread will be more accurate than linearly interpolated yield, particularly with steep interest rate swap curves.

6.5.4 Treasury and Euro Dollar (TED) Spread and LIBOR-OIS Spreads

TED Spread – Calculated as the difference between Libor and the yield on a T-bill of matching maturity. It's an indicator of perceived credit risk in the general economy.

  • TED is an acronym formed from US T-bill and ED, the ticker symbol for the Eurodollar futures contract.
  • An increase (decrease) in the TED spread is a sign that lenders believe the risk of default on interbank loans is increasing (decreasing).

LIBOR-OIS Spread – The difference between Libor and the Overnight Indexed Swap rate. An indicator of the risk and liquidity of money market securities.

  • An OIS is an interest rate swap in which the periodic floating rate of the swap is equal to the geometric average of an overnight rate (or overnight index rate) over every day of the payment period.
  • The index rate is typically the rate for overnight unsecured lending between banks-for example, the federal funds rate for US dollars, Eonia (Euro OverNight Index Average) for euros, and Sonia (Sterling OverNight Index Average) for sterling.

Lesson Wrap-Up

This lesson should leave you able to explain the the swap rate curve: in a fixed-income context and connect it to the decisions made by issuers, investors, or analysts.

Review Prompts

  1. Explain its use in valuation by market participants in your own words.
  2. Explain determination and interpretation of the swap spread for a default-free bond in your own words.
  3. Explain z-spread in your own words.
  4. State one exam-style risk, valuation, or market implication of the the swap rate curve:.