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At the moment I'm working with a banking system that calculates the discounted cash flows of a bond product in the following manner:

It uses the 'regular', exponential way of calculating discounted cash flows which can be translated into this equation:

$$ \frac{1}{(1 + \text{yield})^t} $$

where:

$$t = \frac{\text{number of days between the valuation date and the maturity date}}{\text{number of days in a year}} $$

However, for the last year before the maturity, when $t \leq 1$, it uses the simplified method instead:

$$ \frac{1}{ 1 + \text{yield} \times t} $$

I don't really know why this change in calculations happens, instead of just using the exponential method for all the flows. It is even stranger that it takes the last year and not the last coupon into account.

Does anyone know what financial/business/mathematical reasons could be behind such a behaviour?

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This is simply a market convention. In most bond markets, compounded interest is used when discounting cash flows, EXCEPT when the bond is trading in its final coupon period, at which point simple interest is usually used. This is done to make the yield more comparable to other money market instruments, which are almost always quoted with simple interest.

P.S. I didn't understand the "it takes the last year and not the last coupon into account" part.

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  • $\begingroup$ As you said it would be reasonable if it happened in the last coupon period, but in my case it happens year before the bond maturity date (no matter the coupon period). And this happens for both coupon and zero coupon bonds. $\endgroup$ – Xnn04 Jul 21 '17 at 7:09
  • $\begingroup$ What bond is it (Country, mkt, coupon frequency)? Also, it's always possible that it's just wrong. $\endgroup$ – Helin Jul 21 '17 at 13:34
  • $\begingroup$ Well, I've looked into the source code of the system and it does not differentiate on that basis. This change happens always, for every kind of bond (I also checked this for different bonds with different currency, coupon frequency and so on, it's always the same). It's possible someone made a mistake there. Anyway, would you say that this behavior is acceptable for zero coupon bonds? $\endgroup$ – Xnn04 Jul 21 '17 at 13:42
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    $\begingroup$ I think it's best that you consult with your trader or whoever is using this algo. I've worked at a shop where ALL bonds are ALWAYS discounted using compounded interest, because the traders want it that way. Most other shops allow you to change this behavior through a setting, which is the more sensible thing to do. In the end, it's important to have conversations with end users; they may very well just tell you it's a mistake that needs fixing. $\endgroup$ – Helin Jul 21 '17 at 14:04

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