Swap rates determination

At the inception of the swap, the terms of the swap will be such that the present value of the floating-rate payments is equal to the present value of the fixed-rate payments. That is, the value of the swap is equal to zero at its inception. This is the fundamental principle in determining the swap rate (i.e., the fixed rate that the fixed-rate payer will make). 

It is the same equation as for determining the floating-rate payment except that the swap rate is used instead of the reference rate (3-month EURIBOR in our illustration). 

Let s apply the formula to determine the swap rate for our 3-year swap. Exhibit 19.7 shows the calculation of the denominator of the formula. The forward discount factor for each period shown in Column (5) is obtained from Column (4) of Exhibit 19.6. The sum of the last column in Exhibit 19.7 shows that the denominator of the swap rate formula is 281,764,282. We know from Exhibit 19.6 that the present value of the floating-rate payments is 14,052,917. Therefore, the swap rate is... 

Given the swap rate, the swap spread can be determined. For example, since this is a 3-year swap, the convention is to use the 3-year rate on the euro benchmark yield curve. If the yield on that issue is 4.5875%, the swap spread is 40 basis points (4.9875% - 4.5875%). 

It is not surprising that the net present value is zero. The zero-coupon curve is used to derive the discount factors that are then used to derive the forward rates that are used to determine the swap rate. As with any financial instrument, the fair value is its break-even price or hedge cost. The bank that is pricing this swap could hedge it with a series of FRAs transacted at the forward rates shown. This method is used to price any interest rate swap, even exotic ones. 

Choudhry, M., 2005. An alternative bond relative value measure determining a fair value of the swap spread using libor and gc repo rates. J. Asset Manag. 7 (1), 17-21. 

Asset-swap spread It is determined by combining an interest-rate swap and cash bond. Generally, bonds pay fixed coupons therefore, it will be combined with an interest-rate swap in which the bondholder pays fixed coupons and receives floating coupons. The spread of the floating coupon over an interbank rate is the asset-swap spread. ... 

Suppose that today 3-month EURIBOR is 4.05%. Let s look at what the fixed-rate payer will receive on 31 March of year 1—the date when the first quarterly swap payment is made. There is no uncertainty about what the floating-rate payment will be. In general, the floating-rate payment is determined as follows ... 

Now let s return to our objective of determining the future floating-rate payments. These payments can be locked in over the life of the swap using the EURIBOR futures contract. We will show how these floating-rate payments are computed using this contract. 

Once the swap transaction is completed, changes in market interest rates will change the payments of the floating-rate side of the swap. The value of an interest rate swap is the difference between the present value of the payments of the two sides of the swap. The 3-month EURIBOR forward rates from the current EURIBOR futures contracts are used to (1) calculate the floating-rate payments and (2) determine the discount factors at which to calculate the present value of the payments. 

Recovery rates on bonds vary by the position in the reference entity s capital structure and the level of security offered to the bond holders. Determining the appropriate recovery rate is not a trivial process and requires careful analysis into the traded prices of deliverable obligations for the reference credit. In practice there is limited historical information on the recovery rates experienced for credit default swaps. 

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. 

Note that one does also have an expression for the Kab s) element directly in the evaluated rate matrix K s) above see ref. 9. However, the results above were obtained under the condition that the bath was initially at equilibrium with reactant a). Therefore, unlike K ais) obtained here, the resultant Kat s) is not the thermal backward rate for ft)->(a reaction. It would rather just assume the same expressions above, but swap a and b. Thus, eqn (13.70) could be considered as the general expression for all off-diagonal elements in a thermal rate matrix. The diagonal ones are then determined via the matter conservation law as ... 

A more accurate approach m ht be the one used to price interest tate swaps to calculate the present values of future cash flows usit discount tates determined by the markets view on where interest rates will be at those points. These expected rates ate known as forward interest rates. Forward rates, however, are implied, and a YTM derived using them is as speculative as one calculated using the conventional formula. This is because the real market interest rate at any time is invariably different from the one implied earlier in the forward markets. So a YTM calculation made using forward rates would not equal the yield actually realized either. The zero-coupon rate, it will be demonstrated later, is the true interest tate for any term to maturity. Still, despite the limitations imposed by its underlying assumptions, the YTM is the main measure of return used in the markets. 

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