Swap Pricing

Banks generally use par swap or zero-coupon swap pricing, which is discussed in detail in the next section. This section introduces the subject with an intuitive swap valuation description. 

Consider a vanilla interest-rate swap with a notional principal of M that pays n payments during its life, to a maturity date of T. The date of each payment is on ti with f=l,. . . n. The present value today of a future payment is denoted by PV 0, t). If the swap rate is r, the value of the fixed-leg payments given by (7.2) below. 

The swap valuation is equal to Pyfioat, The swap rate quoted by a 

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Bond Price Swap Price Swap Rate( Redeu-uti ji (i)... 

The cash flows of a typical credit default swap are set out in Exhibit 21.1. Exhibit 21.2 shows the Bloomberg screen CDS for credit default swap prices. 

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). 

As explained in chapter 3, zero-coupon, or spot, rates are true interest rates for their particular terms to maturity. In zero-coupon swap pricing, a bank views every swap, even the most complex, as a series of cash flows. The zero-coupon rate for the term from the present to a cash flows payment date can be used to derive the present value of the cash flow. The sum of these present values is the value of the swap. 

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. 

Grinblatt, M., and N. Jegadeesh. 2000. Futures vs. Forward Prices Implications for Swap Pricing and Derivatives Valuation. In Jegadeesh, N., and B. Tuckman, eds. Advanced Fixed-Income Valuation Tools. New York John Wiley Sons. 

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. 

IrBond Price Swap Price 2 Swap Rate Redenption Preaiua... 

The market approach to CDS pricing adopts the same no-arbitrage concept that is used in interest rate swap pricing. This states that, at inception ... 

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. 

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