Interest rate swaps example

In this way, an interest rate cap allows the borrowing company to benefit when interest rates are low, while protecting the company when interest rates are high. This is marvellous, as it provides the best of both worlds, but such a result does not come free As with other interest rate options, the company would have to pay an up-front premium to purchase the cap. In the example here, this up-front premium might be around 165 bp of the notional principal, i.e., 16,500, which is equivalent to around 35 bp per annum if this cost were spread over the lifetime of the cap. This caps the effective EURIBOR at around 3.35% rather than 3%. Contrast this with the interest rate swap, which does not involve an up-front payment, but penalizes the company with a higher initial interest rate instead. 

The reference rates that have been used for the floating rate in an interest rate swap are various money market rates. The most common in Europe is EURIBOR. EURIBOR is the rate at which prime banks offer to pay on euro deposits available to other prime banks for a given maturity. There is not just one rate but a rate for different maturities. For example, there is a 1-month EURIBOR, 3-month EURIBOR, and 6-month EURIBOR. 

An example would be that a protection buyer holding a fixed-rate risky bond and wishes to hedge the credit risk of this position via a credit default swap. However, by means of an asset swap the protection seller (e.g., a bank) will agree to pay the protection buyer LIBOR +/-spread in return for the cash flows of the risky bond. In this way the protection buyer (investor) may be able to explicitly finance the credit default swap premium from the asset swap spread income if there is a negative basis between them. If the asset swap was terminated, it is common for the buyer of the asset swap package to take the unwind cost of the interest rate swap. 

An interest rate swap is thus an agreement between two parties to exchange a stream of cash flows that are calculated hy applying different interest rates to a notional principal. For example, in a trade between Bank A and Bank B, Bank A may agree to pay fixed semiannual coupons of 10 percent on a notional principal of 1 million in return for receiving from Bank B the prevailing 6-month LIBOR rate applied to the same principal. The known cash flow is Bank As fixed payment of 50,000 every six months to Bank B. 

SPV usually enters into an interest rate swap. The swap counterparty may also sell the SPV other derivative instruments, such as interest rate caps, to manage possible cash flow risk. Such risk-exposure management requires careful attention, since the SPV s risk profile can have a significant impact on the credit risk of the notes issued to investors. In an unleveraged transaction, the size of the issue is equivalent to the credit protection the SPV offers on the reference pool of assets. For example, if the credit default swap is on a nominal of 300,000, the nominal value of the notes issued will be 300,000. 

In selecting the model, a practitioner will select the market variables that are incorporated in the model these can be directly observed such as zero-coupon rates or forward rates, or swap rates, or they can be indeterminate such as the mean of the short rate. The practitioner will then decide the dynamics of these market or state variables, so, for example, the short rate may be assumed to be mean reverting. Finally, the model must be calibrated to market prices so, the model parameter values input must be those that produce market prices as accurately as possible. There are a number of ways that parameters can be estimated the most common techniques of calibrating time series data such as interest rate data are general method of moments and the maximum likelihood method. For information on these estimation methods, refer to the bibliography. 

The two previous chapters introduced and described a fractiOTi of the most important research into interest-rate models that has been carried out since the first model, presented by Oldrich Vasicek, appeared in 1977. These models can be used to price derivative seciuities, and equitibrium models can be used to assess fair value in the bond market. Before this can take place however, a model must be fitted to the yield curve, or calibrated In practice, this is carried out in two ways the most popular approach involves calibrating the model against market interest rates given by instruments such as cash Libor deposits, futures, swaps and bonds. The alternative method is to model the yield curve from the market rates and then calibrate the model to this fitted yield curve. The first approach is common when using, for example extended Vasicek... 

A third methodology uses a simplified approach to get an approximation of the convexity bias. The mean reversion rate, a, typically varies from O.OOf for negligible effects to O.f for high mean reversion. For example, Bloomberg assumes a constant mean reversion rate of 0.03. Observed volatilities of interest rate caps are multiplied by their corresponding swap rates to get an estimate of o. 

The result for the company is that EURIBOR will effectively be collared in the range 2.50% to 3.50%. If EURIBOR ever rose above 3.50%, the company s costs would be capped at that level. The downside is that whenever the EURIBOR setting was below 2.50%, the company would not pay less. As neither the cap nor the collar include the first interest period, the company in this example is assured of six months borrowing based on a EURIBOR of 2%. Thereafter, even if EURIBOR were to stay low, the company s borrowing would be based on a EURIBOR of at least 2.50%. This may nonetheless still prove less expensive than paying the fixed rate of 3% throughout, which is what the swap would involve. 

Notes issued in synthetic structures are organized by tranche. With the proceeds from the notes it issues to investors, the SPV purchases high-quality (AAA) liquid securities—for example, U.S. Treasuries, bank asset-backed paper such as credit card ABS, and German bonds, such as Pfandbriefe —to serve as collateral. This collateral will generate LIBOR-related interest and principal cash flows that the SPV passes on to the investors together with the swap premium, which creates an additional credit spread on the notes. The cash flows from the collateral may not match the payments due on the issued notes—for example, the bonds used as collateral may pay a flxed rate and the issued notes a floating one. To remedy this, the... 

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