Asset-Swap Pricing

Asset-swap pricing is commonly applied to credit-default swaps, especially by risk management departments seeking to price the transactions held on credit traders book. A par asset swap typically combines an interest rate swap with the sale of an asset, such as a fixed-rate corporate bond, at par and with no interest accrued. The coupon on the bond is paid in return for LIBOR plus, if necessary, a spread, known as the asset-swap spread. This spread is the price of the asset swap. It is a function of the credit risk of the underlying asset. That makes it suitable as the basis for the price payable on a credit default swap written on that asset. 

The asset swap spread is equal to the underlying asset s redemption yield spread over the government benchmark, minus the spread on the associated interest rate swap. The latter, which reflects the cost of convert- 

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The asset swap price (i.e., spread) on this bond has the following components ... 

See Moorad Choudhry, Issues in the Asset Swap Pricing of Credit Default Swaps, in Frank J. Fabozzi (editor), Professional Perspectives on Fixed Income Portfolio Management Volume 4 (Hoboken, NJ John Wiley Sons, Inc., 2003). 

Bloomberg users can use screen VCDS to obtain a CDS-price implied bond valuation, which can be compared to the actual market-observed asset swap price for a bond. This can then be used as a measure of relative value. 

The spread of the floating coupon over the bond s market price, that is the asset-swap value is the difference between the bond s market price and par. The package of the asset swap is structured in two phases ... 

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. 

As shown in Eigures 1.4 and 1.5, with this swap structuring, the asset-swap spread for HERIM is 39.5 bp and for TKAAV is 39.1 bp. These represent the spreads that will be received if each bond is purchased as an asset-swap package. In other words, the ASW spread provides a measure of the difference between the market price of the bond and the value of the cash flows evaluated using zero-coupon rates. 

However, a critical issue on this spread measure is how the asset swap has been stmctured. ASW measure works very well when bond prices trade at or near to par. Most corporate bonds trade with price away from the par (as in this case), thus making the ASW an inaccurate spread measure. If the bond trades at premium, the ASW spread will overestimate the level of credit risk conversely, if the bond trades at discount the ASW spread will underestimate the level of credit risk. Therefore, in the case of HERIM and TKAAV, the ASW spread overestimates the credit risk associated with the bonds because both trade significantly at premium. 

A credit default swap (CDS) price provides fundamental credit risk information of a specific reference entity or asset. As explained before, asset swaps are used to transform the cash flows of a corporate bond for interest rate hedging purpose. Since the asset swaps are priced at a spread over the interbank rate, the ASW spread is the credit risk of the same one. However, market evidence shows that credit default swaps trade at a different level to asset swaps due to technical... 

If this difference is positive we have a positive basis, and it happens when credit derivates trade at higher prices than asset swaps. Otherwise, if the difference is negative we have a negative basis. Consider the following example of a positive basis trade for HERIM and TKAAV. For both bonds, we calculate the CDS spread which is equal to 86.3 for HERIM and equal to 88.6 for TKAAV. The CDS basis over the ASW spread determined before is equal to 46.8 for HERIM and equal to 49.5 for TKAAV. However, the basis illustrated in Figure 1.6 is different because CRVD measures them relative to the Z-spread, which is 50.7 for HERIM and 48 for TKAAV. The basis relative to the Z-spread is equal to 35.6 for HERIM and 40.6 for TKAAV. So, we note that either the ASW spread or the Z-spread can be used as the basis performance, giving a similar result and positive basis in both cases. 

We assume we have constructed a market curve of Libor discount factors where Df(t) is the price today of 1 to be paid at time t. From the perspective of the asset swap seller, it sells the bond for par plus accrued interest. The net up-front payment has a value 100 F where P is the market price of the bond. If we assume both parties to the swap are interbank credit quality, we can price the cash flows off the Libor curve. 

Figure 8.2 shows the Bloomberg YAS page for Tesco bond SVi% 2019, as at October 9, 2014. The bond has a price of 109.345 and yield to maturity of 3.46%. On the date, the yield spread over a government bond benchmark UK 41 % Treasury 2019 is 200 basis points. The G-spread over an interpolated government bond is 181.5 basis points. Conventionally, the difference between these two spreads is narrow. We see also that the asset-swap spread is 173.6 basis points and Z-spread is 166.3 basis points. 

Asset swaps are used to alter the cash flow profile of a bond. The asset swap market is an important segment of the credit derivatives market since it explicitly sets out the price of credit as a spread over LIBOR. Pricing a bond by reference to LIBOR is commonly used and the spread over LIBOR is a measure of credit risk in the cash flow of the underlying... 

The accrued interest and the clean price premium or discount compared to par value. Thus when pricing the asset swap it is necessary to compare the par value and to the underlying bond price. 

The Bloomberg asset swap calculator pricing screen at Exhibit 21.17 shows these components in the analysis of the swapped spread details. Exhibit 21.18 shows an example of an asset swap calcnlation. 

CDS prices are often compared to bond asset swap levels in order to gain an initial comparison of the credit quality implied by the market. In fact, differences do exist between the CDS spread and the asset swap spread, even though both spreads may be viewed as compensating the... 

Return from a holding of fixed-income securities may be measured in more than one way. The most common approach is to consider the asset-swap spread. More sophisticated investors also consider the basis spread between the cash bond and the same-name credit default swap price, which is known as the basis. In this chapter we consider the most accessible way to measure bond return. 

The I-spread is sometimes used to compare a cash bond with its equivalent CDS price, but for straightforward relative value analysis is usually dropped in favor of the asset-swap spread, which we look at later in this section. 

An asset swap is a package that combines an interest-rate swap with a cash bond, the effect of the combined package being able to transform the interest-rate basis of the bond. Typically, a fixed-rate bond will be combined with an interest-rate swap in which the bond holder pays fixed coupon and received floating coupon. The floating coupon will be a spread over LIBOR (see Choudhry et al. 2001). This spread is the asset-swap spread and is a function of the credit risk of the bond over and above interbank credit risk. Asset swaps may be transacted at par or at the bond s market price, usually par. This means that the asset swap value is made up of the difference between the bond s market price and par, as well as the difference between the bond coupon and the swap flxed rate. 

Put simply, the Z-spread is the basis point spread that would need to be added to the implied spot yield curve such that the discounted cash flows of the bond are equal to its present value (its current market price). Each bond cash flow is discounted by the relevant spot rate for its maturity term. How does this differ from the conventional asset-swap spread Essentially, in its use of zero-coupon rates when assigning a value to a bond. Each cash flow is discounted using its own particular zero-coupon rate. The bond s price at any time can be taken to be the market s value... 

FIGURE 19.7 Bloomberg Graph Using Screen G , Plot of Asset-Swap Spread and CDS Price for GKN Bond, April-September 2005 ... 

The implications of this new model class are in contrast to most term structure models discussed in the literature, which assume that the bond markets are complete and fixed income derivatives are redundant securities. Collin-Dufresne and Goldstein [ 18] and Heiddari and Wu [36] show in an empirical work, using data of swap rates and caps/floors that there is evidence for one additional state variable that drives the volatility of the forward rates. Following from that empirical findings, they conclude that the bond market do not span all risks driving the term structure. This framework is rather similar to the affine models of equity derivatives, where the volatility of the underlying asset price dynamics is driven by a subordinated stochastic volatility process (see e.g. Heston [38], Stein and Stein [71] and Schobel and Zhu [69]). 

Jamshidian, F., 1997. LIBOR and swap market models and measures. Finance Stochast. 1,293-330. Jarrow, R., Madan, D., 1991. Option Pricing Using the Term Structure of Interest Rates to Hedge Systematic Discontinuities in Asset Returns Working Paper. Cornell University, Ithaca, NY,... 

Exhibit 21.4 illustrates a generic TR swap. The protection buyer has contracted to pay the total return on a specified reference asset, while simultaneously receiving a LIBOR-based return from the protection seller. The reference or underlying asset can be a bank loan such as a corporate loan or a sovereign or corporate bond. The total return payments include the interest payments on the underlying loan as well as any appreciation in the market value of the asset. The protection seller will pay the LIBOR-based return it will also pay any difference if there is a depreciation in the price of the asset. The economic effect is as if this entity owned the underlying asset, as such TR swaps are synthetic loans or securities. 

Although the pricing of a credit default swap can be numerically reduced to a model, the inputs to that model still remain subjective. How can one calculate an exact valne for R, the recovery value of an issuer s assets post-default Or, more importantly, how can one calculate the hazard rate X for an issuer What is the probability that a particular issuer will default in five years Determining the true credit risk of an issuer has been a topic of intense focus in recent years and, as a result, quite a variety of methods and models have surfaced. 

In a default, the swap is terminated, and the default payment is calculated and handed over. The amount of this payment may be linked to the change in price of the reference asset or another specified asset or fixed at a predetermined recovery rate. Alternatively, it may involve actual delivery of the reference asset at a specified price. 

If a credit event occurs, the SPV usually pays out a cash amount equal to the par value of the underlying assets covered by the credit default swap, less their post-default price. Less commonly, the SPV physically settles the credit-default swap by purchasing the defaulted assets at par value. The credit loss is then passed on to the investors according to the priority of the tranches they hold. 

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