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Why LIBOR and Continuous-Compounding Discount Factors Differ

Article Quant Q&A · Author: user13232877
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Summary

The document raises a fixed-income question about why discount factors for the same maturity and market date differ when one is reported using LIBOR conventions and another using continuous compounding. It cites two tables from a reference text and notes that the figures are close but not identical, despite the expectation that no-arbitrage pricing should give the same discount value.

The question highlights the role of compounding frequency and yield conversion in calculating discount factors. However, the text does not provide an answer or show how the quoted LIBOR discount factor is derived. It therefore offers a useful conceptual prompt about comparing rate conventions, but leaves the calculation and reconciliation unresolved.

Key ideas

  • Discount factors for the same maturity can differ when expressed under different compounding conventions.
  • No-arbitrage comparisons require consistent treatment of rates and compounding frequency.
  • The document provides example figures from a reference text but does not derive them.
  • The underlying question remains unanswered in the supplied material.

Tags

Fixed incomeStatistics
Full text
# Why LIBOR discount and continuous compounding discount are different?


# Why LIBOR discount and continuous compounding discount are different?












The reference is Fixed Income Securities by Pietro Veronesi.

As you can see, In Table 20.5 when the maturity is 1.25, the LIBOR Discount is 96.7402 However In Table 20.3 with same maturity, the continuous compounding discount is 96.7385

Even it is the data from same date November 1, 2004

I think those two should be the same for no arbitrage. I already know when the frequency is changed, the yield should also be changed. But the background is that : Because the discount is same, the only one source that makes the difference is 'frequency'.

So I think although the frequency of LIBOR discount is different with Continuously compounding, the discount should be the same.

How it is derived the number 96.7402?

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