Swap Valuation

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

Consider a plain vanilla interest rate swap with a notional principal of M that pays n interest payments through its maturity date, T. Payments are made on dates 4 where i = 1,. ..n. The present value today of a future payment made at time r, is denoted as PV 0, t,). If the swap rate is r, the present value of the fixed-leg payments, PVfi s is given by equation (7.2). 

The value of an existing swap s floating-leg payments on date is given by equation (7-3). 

The present value at time 0 of the floating-rate payment is given by equation (7.4). 

For a new swap, the present value as of of the floating payments is given by equation (7.5). 

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While it is not uncommon for active market makers and end users to utilize their own, customized set of tools for credit default swap valuation, many, if not all of these methodologies arise from the same general framework and ask the same two questions What is the probability that a particular issuer will default and, Upon the occurrence of a default event, what does one expect to recover from an issuer ... 

The swap valuation is equal to - PVfl . The swap rate quoted... 

The zero-coupon curve is used in the asset swap valuation. This curve is derived from the swap curve, so it is the implied zero-coupon curve. The asset swap spread is the spread that equates the difference between the present value of the bond s cash flows, calculated using the swap zero rates, and the market price of the bond. This spread is a function of the bond s market price and yield, its cash flows, and the implied zero-coupon interest rates. ... 

There is still a consistency problem if we want to price interest rate derivatives on zero bonds, like caplets or floorlets, and on swaps, like swaptions, at the same time within one model. The popular market models concentrate either on the valuation of caps and floors or on swaptions, respectively. Musiela and Rutkowski (2005) put it this way We conclude that lognormal market models of forward LIBORs and forward swap rates are inherently inconsistent with each other. A challenging practical question of the choice of a benchmark model for simultaneous pricing and hedging of LIBOR and swap derivatives thus arises. ... 

Craisider a hypothetical situation. Assume that an option-free bond paying a semi-annual coupon 5.5% on par value, with a maturity of 5 years and discount rate of 8.04% (EUR 5-year swap rate of 1.04% plus credit spread of 700 basis points). Therefore, the valuation of a conventional bond is performed as follows (Figure 9.4). 

What is worthy then of a further investment of cash to purchase this second edition Hopefully the new chapters on asset swap spread relative value, convertible bonds, callable/putable bonds and floating-rate notes will be sufficient justification additionally we have updated the previous chapters on inflation-linked bonds and risky corporate bonds valuation. We have also included Excel spreadsheets that enable the reader to apply the analysis described in the chapters right away to bonds that he or she selects. 

It is important for a zero-coupon yield curve to be constructed as accurately as possible. This because the curve is used in the valuation of a wide range of instruments, not only conventional cash market coupon bonds, which we can value using the appropriate spot rate for each cash flow, but other interest-rate products such as swaps. 

The fundamental principle of valuation is that the value of any financial asset is equal to the present value of its expected future cash flows. This principle holds for any financial asset from zero-coupon bonds to interest rate swaps. Thus, the valuation of a financial asset involves the following three steps ... 

The same valuation principle applies to more complicated swaps. For example, there are swaps whose notional amount changes in a predetermined way over the life of the swap. These include amortizing swaps, accreting swaps, and roller coaster swaps. Once the payments are specified, the present value is calculated as described above by simply adjusting the payment amounts by the changing notional amounts— the methodology does not change. 

Cash settlement represents another method of settling credit derivative transactions. In cash settlement, the protection buyer will receive an amount based on the difference between par and the valuation of the reference asset at a given valuation date, as agreed in the credit default swap contract. 

A credit default swap has two valuation legs, the fee leg and the contingent leg. We can develop an equation of value which describes the valuation of the credit default swap (assuming a deterministic recovery rate) as... 

While the answers to these questions are not always readily apparent in the market, there exist many methods for their computation. Some are relatively simple while others are complex, but the valuation of a default swap is most easily understood if approached backwards, such that we assume the answers to these questions are already known. Once the reader has an understanding of the valuation theory it will be easier to approach these fundamental questions head on. 

This chapter discusses the uses of interest rate swaps, including as a hedging tool, from the point of view of bond-market participants. The discussion touches on pricing, valuation, and credit risk, but for complete... 

As noted earlier,a newly transacted interest rate swap denotes calculating the swap rate that sets the net present value of the cash flows to zero. Valuation signifies the process of calculating the net present value of an existing swap by setting its fixed rate at the current market rate. Consider a plain vanilla interest rate swap with the following terms ... 

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. 

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