Interpreting Tenor-Specific LIBOR Pseudo-Discount Curves

Summary

The document asks how to derive a zero-coupon curve for a particular LIBOR tenor from that tenor’s forward curve. It proposes a relationship between forward rates and discount factors at the start and end of each accrual period, then asks what the resulting discount factor represents. The answer identifies this as a pseudo-discount curve: a curve that can be used to calculate corresponding LIBOR forward rates and LIBOR zero rates.

The key distinction is between this tenor-specific construct and the true discount curve. The answer says that the true discounting curve is the OIS curve, built independently from the LIBOR curve. This is a brief conceptual explanation rather than a derivation or calibration guide. It does not discuss curve construction details, market conventions, or how to handle differences among tenors, so those points would need separate treatment in practical pricing work.

Key ideas

• A forward curve is specific to its underlying LIBOR tenor.
• The proposed discount factors define a pseudo-discount curve for that tenor.
• The pseudo-discount curve can produce related LIBOR forward and zero rates.
• The answer distinguishes LIBOR pseudo-discounting from true OIS discounting.
• The document gives no detailed calibration procedure or convention guidance.

Tags

# LIBOR with different tenor


# LIBOR with different tenor












Let $F(t;S,T)$ be the forward rate from $S$ to $T$ seen at time $t$, and $I$ be one of tenors, i.e. $I$ is one of {1M, 3M, 6M, 12M}. Then the forward curve $t\mapsto F(0;t,t+I)$ is $I$-forward curve.

I understand that the forward curve above is easy to calibrate to market values that involves LIBOR of tenor $I$, such as swaps. But how can I get $I$-discounting curve (zero coupon curve) from the forward curve? Is it simply to find the function $P_I(0,t)$ that satisfies the following equation? $$F(0;t,t+I)=\frac{1}{I}\bigg(\frac{P_I(0,t)}{P_I(0,t+I)}-1\bigg)$$

If this is the case, what is the meaning of the value $P_I(0,t)$? Is it simply a function gives the forward curve back?

## Answer by Helin (score 1)

https://quant.stackexchange.com/a/18453

Your $P_I(t,T)$ is the formula for the so-called "pseudo" discount curve. It can be used to compute relevant LIBOR forward rates and LIBOR zero rates.

The "true" discount curve is of course the OIS discount curve, which can be built independently of the LIBOR curve.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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