Differential risk annuity

A differential risk annuity that delivers payments equal to the difference between the quoted margin and the required margin multiplied by the par value. 

Note it is the differential risk annuity that causes the floater s price to deviate from par on a coupon reset date. Specifically, if the required... 

Exhibit 3.7 illustrates the calculation. Once again for simplicity, we assume that 3-month LIBOR remains unchanged at 5% and there are 91 days in each coupon period. Since a risky floater can be thought of as par plus the differential risk annuity, all that is necessary is to take the present value of the annuity. Each annuity payment is computed as follows ... 

The quoted margin and required margin are in Columns (4) and (5), respectively. These cash flows are contained in Column (6). The discount factors are computed as described previously with the exception of the larger required margin. The discount factors appear in Column (7). The present value of the each cash flow is in Column (8) and is just the product of the cash flow (Column (6)) and its corresponding discount factor (Column (7)). The present value of the differential risk annuity is -0.1813 and is shown at the bottom of Column (8). 

EXHIBIT 8.7 Valuing the Differential Risk Annuity When the Market s Required Margin Is Greater Than the Quoted Margin ... 

Once the present valne of the differential risk annuity is determined, the price of our hypothetical 4-year floater is simply the sum of 100 (price of the floater per 100 of par value when the quoted margin and required margin are the same) and the present value of the differential risk annuity. In our example,... 

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