Cashflow valuation

[kea]

Hi, I’m trying to figure out whether there’s a way of specifying whether a fixed interest rate calculation should use zero coupon-like calculation, or a simple interest calculation? I might be overlooking something really obvious, but I haven’t found anything yet… I could derive it from the tenor of the calculation period, but I could have period that are less than one year and still use ZC-like calculation (that is, notional * ((1+r)^t – 1), where t is the relevant daycount fraction) as opposed to a simple-IR one (notional*r*t). An example are RPI ZC swaps where the fixed side is calculated as a ZC, and in structures I can well have t that is less than one (a revenue swap with quarterly flows would be a good example). I’d be grateful for any help. Regards, Vlad

[mgratacos]

Vlad, I am not sure I understand your question but did you take a look at the example called inflation-swap-ex05-zc.xml inside the inflation-swaps folder? It’s an RPI ZC swap with a ZC fixed leg and a floating leg calculating quarterly and paying annually. You can play around with the calculation and payment frequencies in order to represent the behavior of your product. Hope this helps. Marc

[kea]

Hi Marc, I saw how the zc’s are represented in the examples, but that doesn’t solve my problem (or, at least, I don’t see how it does). In fact, I’m not sure about the parts of the example – although the bits I don’t understand in the RPI example are on the RPI leg so it’s not relevant to my problem. That said, I will go through that as well, below, but first I will address my fixed leg problem. The example says: 30 Y 22 The method for calculating the flow (on unit notional) is zero-coupon, which is (1+fixed rate) ^ T – 1, where T is the lenght of the period in the relevant daycount. Say here it’s 22. Now imagine, that you want a shorter period, like half a year, so you’d have a claculationPeriodFrequency like: 6 M 22 T here would be 0.5 (for argument’s sake), so the value paid out (at the end of this period) would be (1+fixed rate)^0.5 – 1, which is quite different from the value of what a vanilla interest rate swap with this calculation period would pay (i.e. fixed rate * 0.5) My question is whether there’s any way of distinguishing these two, so I can tell – without going up all the way to the product (even that might not help as I might have a structure of swap streams where some are simple-interest-swap-streams, and some are zc-like swap streams) – which formula should I use. I can even come up with a pure interest-rates example, where one side pays a bullet ZC payment at the end, and the other pays fixed/floating side on the other leg. You could try to imply the formula from the tenor of the ZC payment’s calculation method, but the problem is that the tenor could be quite short – less than a year, and how you’d distinguish it from a “normal” zc swap then? It’s not uncommon in the inflation world that the T in the (1+rate)^T formula is actually specified in a form of schedule – of course, not for a single ZC swap, but for an inflation revenue swap. [off topic] Now, to the RPI leg and the weirdness (IMO) of the example. RPI ZC swaps calculate only once in its life for both legs. For example, if I enter into a market RPI ZC swap today, with a yearly tenor, it will: – use October 2007 RPI as a base RPI (easy to capture in FPML)- let’s call this I_start – use October 2008 RPI as the final RPI – with calculation date being (say) 7 December 2008, and RPI lag 2. let’s call it I_end The only calculation on this leg is done at the end (typically the date of the payment, for the market-vanilla RPI ZC swaps), and the calculation is (I_end/I_start – 1)* notional. If it was as you say calculating quarterly and paying annually, it wouldn’t be a ZC swap – it’s like saying that a (normal) ZC bond calculates quarterly and pays annually… At the best, it could be a revenue swap, which is a stream of RPI ZC cashflows, but they still calculate at payment date of the individual flows. Regards, Vlad

[mgratacos]

You’ll always have to go to the product to compare the calculation frequency and the payment frequency. Only doing that you’ll be able to determine whether there is compounding in any of the legs.

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