Bond Discounting Conventions in the Final Coupon Period

Summary

The document asks why a bond pricing system switches discount factors during the final year before maturity. It contrasts annual compounding, using a factor based on yield raised over the time to payment, with simple-interest discounting, using yield multiplied by the year fraction. The question also wonders why the switch is tied to a year rather than the final coupon period.

The answer identifies the change as a market convention: bond cash flows are generally discounted with compounding, but simple interest is commonly used when the bond is in its final coupon period. The stated rationale is to make the yield more comparable with money-market instruments, which are usually quoted using simple interest. The response does not provide a mathematical derivation or survey particular market rules, and it does not resolve the question’s distinction between a final year and a final coupon period. Actual conventions may depend on the relevant market and instrument, so the explanation should not be treated as universal.

Key ideas

• The question contrasts compounded discounting with simple-interest discounting for near-maturity cash flows.
• The response describes simple interest during a bond’s final coupon period as a market convention.
• The convention is linked to comparability with money-market instruments that commonly use simple-interest quotations.
• The discussion does not establish a universal rule or explain why the question’s system uses a final-year threshold.

Tags

# Discounted cash flows for bond valuation: exponential and simplified


# Discounted cash flows for bond valuation: exponential and simplified












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?

## Answer by Helin (score 2, accepted)

https://quant.stackexchange.com/a/35200

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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