Swap curves

The zero-coupon curve is used in the asset-swap analysis, in which the curve is derived from the swap curve. Then, the asset-swap spread is the spread that allows us to receive the equivalence between the present value of cash flows and the current market price of the bond. 

Making comparison between bonds could be difficult and several aspects must be considered. One of these is the bond s maturity. For instance, we know that the yield for a bond that matures in 10 years is not the same compared to the one that matures in 30 years. Therefore, it is important to have a reference yield curve and smooth that for comparison purposes. However, there are other features that affect the bond s comparison such as coupon size and structure, liquidity, embedded options and others. These other features increase the curve fitting and the bond s comparison analysis. In this case, the swap curve represents an objective tool to understand the richness and cheapness in bond market. According to O Kane and Sen (2005), the asset-swap spread is calculated as the difference between the bond s value on the par swap curve and the bond s market value, divided by the sensitivity of 1 bp over the par swap. 

Euro swap curve as reference interbank curve, coherent with the bond s currency (EUR). 

Z-spread is an alternative spread measure to the ASW spread. This type of spread uses the zero-coupon yield curve to calculate the spread, in which in this case is assimilated to the interest-rate swap curve. Z-spread represents the spread needful in order to obtain the equivalence between the present value of the bond s cash flows and its current market price. However, conversely to the ASW spread, the Z-spread is a constant measme. 

Another approach is to compare the floating-rate note with a derived yield of a fixed-rate bond by using an interest rate swap curve matched with floater coupons. Figure 10.4 shows the Bloomberg YASN screen for Mediobanca float... 

In some European countries, swap curves are used as a benchmark for pricing securities. 

The minimum interest rate that an investor should require is the yield available in the marketplace on a default-free cash flow. For bonds whose cash flows are denominated in euros, yields on European government securities serve as benchmarks for default-free interest rates. In some European countries, the swap curve serves as a benchmark for pricing spread product (e.g., corporate bonds). For now, we can think of the minimum interest rate that investors require as the yield on a comparable maturity benchmark security. 

A Z-spread can be calculated relative to any benchmark spot rate curve in the same manner. The question arises what does the Z-spread mean when the benchmark is not the euro benchmark spot rate curve (i.e., default-free spot rate curve) This is especially true in Europe where swaps curves are commonly used as a benchmark for pricing. When the government spot rate curve is the benchmark, we indicated that the Z-spread for nongovernment issues captured credit risk, liquidity risk, and any option risks. When the benchmark is the spot rate curve for the issuer, for example, the Z-spread reflects the spread attributable to the issue s liquidity risk and any option risks. Accordingly, when a Z-spread is cited, it must be cited relative to some benchmark spot rate curve. This is essential because it indicates the credit and sector risks that are being considered when the Z-spread is calculated. Vendors of analytical systems such Bloomberg commonly allow the user to select a benchmark. 

The terms spread or credit spread refer to the yield differential, usually expressed in basis points, between a corporate bond and an equivalent maturity government security or point on the government curve. It can also be expressed as a spread over the swap curve. In the former case, we refer to the fixed-rate spread. In the latter, we use the term spread over EURIBOR, or over the swap curve. 

In the pre-euro days, traders were usually organized by currency. Now, sector specialization is the rule. For most issues, buy or sell indications are initially indicated on a spread basis. The spread can be either over the swap curve or over a specified government benchmark. A corporate bond issue keeps the same benchmark for its entire life they roll down the curve together. This is in contrast to the United States, where the convention is to quote a corporate bond s spread over the nearest on-the-run (most recently issued) 2-, 5-, 10-, or 30-year maturity Treasury bond. 

The swap curve depicts the relationship between the term structure and swap rates. The swap curve consists of observed market interest rates, derived from market instruments that represent the most liquid and dominant instruments for their respective time horizons, bootstrapped and combined using an interpolation algorithm. This section describes a complete methodology for the construction of the swap term structure. 

In deriving the swap curve, the inputs should cover the complete term structure (i.e., short-, middle-, and long-term parts). The inputs should be observable, liquid, and with similar credit properties. Using an interpolation methodology, the inputs should form a complete, consistent, and smooth yield curve that closely tracks observed market data. Once the complete swap term structure is derived, an instrument is marked to market by extracting the appropriate rates off the derived curve. 

The technique for constructing the swap term structure, as constructed by market participants for marking to market purposes, divides the curve into three term buckets. The short end of the swap term structure is derived using interbank deposit rates. The middle area of the swap curve is derived from either forward rate agreements (FRAs) or interest rate futures contracts. The latter requires a convexity adjustment to render it equivalent to FRAs. The long end of the term structure is constructed using swap par rates derived from the swap market. 

A combination of the different interest rates forms the basis for the swap curve term structure. For currencies where the future or forward... 

To derive the swap term structure, observed market interest rates combined with interpolation techniques are used also, dates are constructed using the applicable business-day convention. Swaps are frequently con-strncted nsing the modified following bnsiness-day convention, where the cash flow occurs on the next business day unless that day falls in a different month. In that case, the cash flow occurs on the immediately preceding business day to keep payment dates in the same month. The swap curve yield calculation convention frequently differs by currency. Exhibit 20.2 lists the different payment frequencies, compounding frequencies, and day count conventions, as applicable to each currency-specific interest rate type. 

The short end of the swap curve, out to three months, is based on the overnight, 1-month, 2-month, and 3-month deposit rates. The short-end deposit rates are inherently zero-coupon rates and need only be converted to the base currency swap rate compounding frequency and day count convention. The following equation is solved to compute the continuously compounded zero-swap rate (r ) ... 

The long end of the swap curve is derived directly from observable coupon swap rates. These are generic plain vanilla interest rate swaps with fixed rates exchanged for floating interest rates. The fixed swap rates are quoted as par rates and are usually compounded semiannually (see Exhibit 20.2). The bootstrap method is used to derive zero-coupon interest rates from the swap par rates. Starting from the first swap rate, given all the continuously compounded zero rates for the coupon cash flows prior to maturity, the continuously compounded zero rate for the term of the swap is bootstrapped as follows ... 

Progressing recursively along the observed swap rates interpolating between market observations as required forms the complete long end of the swap curve. 

The credit curves (or default swap curves) reflect the term structure of spreads by maturity (or tenor) in the credit default swap markets. The shape of the credit curves are influenced by the demand and supply for credit protection in the credit default swaps market and reflect the credit quality of the reference entities (both specific and systematic risk). The changing levels of credit curves provide traders and arbitragers with the opportunity to measure relative value and establish credit positions. 

Z-spread is the spread over the zero-swap curve hy which the bond cash flows can be discounted to get the current market price... 

First, as mentioned earlier, there is usually no universal benchmark in a given market. Again, a possible approach, used in Barra s models, is to introduce a swap spread factor that describes the average spread between sovereign and swap rates and can conveniently allow spread risk to be expressed with respect to the LIBOR/swap curve when interest rate risk factors are originally based on the sovereign yield curve. 

Credit spreads are computed with respect to the local swap curve to accommodate for the swap spread factor. 

Benchmark SEE lilPsk EU BGN Swap Curve Sprds User [ ]flsk... 

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