Rate Swap Applications

This section discusses how swaps are used to hedge bond instruments and how swap books are themselves hedged. 

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One straightforward application of an interest rate swap is to convert a floating-rate liability into a fixed-rate one, usually in an effort to remove exposure to anticipated upward moves in interest rates. Say a company has borrowed money at a floating rate of 100 basis points over sbc-month LIBOR. Fearing that interest rates will rise in the three years remaining on the loan, it enters into a three-year semiannual interest rate swap with a bank, depicted in FIGURE 7.8, in which it pays a fixed rate of 6.75 percent and receives six-month LIBOR. This fixes the company s borrowing costs for three years at 6.75 percent plus 100 basis points, or 7-75 percent, for an effective annual rate of 7-99 percent. 

Several factors affect the performance of HPTMC. First, factors that affect the performance of the underling expanded ensemble simulation clearly influence the performance of HPTMC. With regard to HPTMC itself, the frequency and success rate of configuration swaps are the most important factors. A simple rule-of-thumb that we have adopted in these applications is to make the frequency of successful swaps of the same order of magnitude as the frequency of successful particle insertions/removals. Note, however, that simulations of different complex fluids are likely to require some fine-tuning to arrive at optimal parallel tempering algorithms for complex fluids. 

To derive the swap term structure, observed market interest rates combined with interpolation techniques are used also, dates are constructed using the applicable business-day convention. Swaps are frequently con-strncted nsing the modified following bnsiness-day convention, where the cash flow occurs on the next business day unless that day falls in a different month. In that case, the cash flow occurs on the immediately preceding business day to keep payment dates in the same month. The swap curve yield calculation convention frequently differs by currency. Exhibit 20.2 lists the different payment frequencies, compounding frequencies, and day count conventions, as applicable to each currency-specific interest rate type. 

A swap s fixed-rate payments are known in advance, so deriving their present values is a straightforward process. In contrast, the floating rates, by definition, are not known in advance, so the swap bank predicts them using the forward rates applicable at each payment date. The fotward rates are those that are implied from current spot rates. These are calculated using equation (7.6). 

Some of the newer models refer to parameters that are difficult to observe or measure direcdy. In practice, this limits their application much as B-S is limited. Usually the problem has to do with calibratii the model properly, which is crucial to implementing it. Galibration entails inputtii actual market data to create the parameters for calculating prices. A model for calculating the prices of options in the U.S. market, for example, would use U.S. dollar money market, futures, and swap rates to build the zero-coupon yield curve. Multifactor models in the mold of Heath-Jarrow-Morton employ the correlation coefficients between forward rates and the term structure to calculate the volatility inputs for their price calculations. 

TR swaps may also be used for speculation. Bond traders who believe that a particular bond not currently on their books is about to decline in price have a couple of ways to profit from this view. One method is to sell the bond short and cover their position through a repo. The cash flow to the traders from this transaction consists of the coupon on the bond that they owe as a result of the short sale and, if the shorted bond falls in price as expected, the capital gain from the short sale plus the repo rate—say, LIBOR plus a spread. The danger in this transaction is that if the shorted bond must be covered through a repo at the special rate instead of the higher general collateral rate—the one applicable to Treasury securities— the traders will be funding it at a loss. The yield on the bond must also be lower than the repo rate. 

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