Why Irregular Cashflows Do Not Determine a Spot Rate by Themselves

Summary

The document raises a curve-construction question involving two cashflows at different times: an earlier zero-coupon payment with a stated spot rate and a later coupon with an unknown rate. It asks whether the earlier rate can be used to infer the later rate, and whether the cashflows should be recast as a coupon bond. The concern is that spot rates should not depend on the size of a cashflow.

No answer or worked calculation is included, so the document does not establish a method for bootstrapping the missing rate. In general, a spot rate is inferred from instrument prices and cashflow structure, and the quoted information here is insufficient to determine one without additional price, discounting, or instrument details. The question is useful as a prompt about distinguishing cashflow amounts from curve inputs, but it offers no evidence, resolution, or stated assumptions about compounding conventions.

Key ideas

• The question asks how to infer a spot rate for a later irregular cashflow from an earlier known rate.
• It considers whether to represent the cashflows as a coupon bond during bootstrapping.
• The document provides no answer, and the stated information alone does not establish a unique rate.

Tags

# Bootstrapping when cashflows are irregular


# Bootstrapping when cashflows are irregular












EDIT: this question was previously closed because it was 'assumed that it should be common knowledge'. I advise you to READ THE QUESTION PROPERLY and you will find out is is NOT common knowledge at all, due to the fact this is a particular case of bootstrapping. In regular bootstrapping you would have a bond and spot rates for all coupon cashflows before it. Here, on the other hand, you have the inverse: a final coupon, for which you don't have the spot rate, and a bond for which you do. Again, read the question properly then give me an explanation, don't come to hasty conclusions: even your certainties may be wrong.

QUESTION:

I have 2 cashflows. One is a zero-coupon bond, the other is a coupon.

```
    t    cashflow   Spot_Rate
0  0.05    101.1       -0.51
1  0.08     0.9         ?
```

How do I calculate spot rate for the second cashflow using the first spot rate?

Thought: Would I have to create a bond which pays (100+0.9) in t=0.08 and a coupon of 0.9 in 0.05 like so?

This strikes me as strange as - in theory - spot rates wouldn't depend on the entity of the cashflow.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.