Quarterly actual/360 basis

The word approximately is used several times in this example because we are using a real-world scenario—one where premium is not paid in continuous time but instead on a quarterly actual/360 basis. This example combines the best of both worlds by using continuous time probability theory but applying it to the real-word conventions and idiosyncrasies of credit default swaps. 

The buyer of protection pays to the seller a periodic premium, often quarterly, and expressed on a per annum basis. The actual cash amounts of all future premium payments are always known, since the terms of the default swap are set on the trade date. Therefore, we can think of these payments as a series of cash flows and value them according to the method above. We define d to be a function representing the number of calendar days since the inception of the default swap. We then define an integer variable / to represent each premium payment date, such that d is a function of /, d(j). Time is also a function of /, and that is simply the number of years from t = 0 until t = j For our sample 2-year credit default swap, the dates are shown in Exhibit 22.2. 

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