Diagnosing Swaption Volatility and Curve Data Inconsistency
Summary
The document asks why swap rates recomputed from Bloomberg curve data do not exactly match the at-the-money strikes in a swaption volatility cube. It outlines two attempted checks: deriving swap rates from forward Libor rates implied by discount factors, and reconstructing discount factors from quoted zero rates. Both methods produce values close to Bloomberg’s, with a reported relative difference of about one percent at most. The question raises day-count conventions and other setup differences as possible causes.
The response suggests checking whether Bloomberg uses dual-curve bootstrapping and OIS discounting. If a user assumes one curve for both forwarding and discounting while the vendor uses separate curves, the mismatch may follow from that modeling difference. The document cautions that unreplicated swaption prices can undermine hedging, though it does not establish which convention caused the specific discrepancy or give a complete reconciliation procedure. The discussion concerns consistency checks before calibrating a Libor market model.
Key ideas
- Recompute at-the-money swap rates from the same curve inputs used to build the swaption volatility cube.
- Differences in day-count conventions or curve construction can create mismatches between quoted and reconstructed values.
- Dual-curve bootstrapping and OIS discounting may explain discrepancies when forwarding and discounting assumptions differ.
- Failure to reproduce market swaption prices can create risks for calibration and hedging.
Tags
Full text
# Incoherence in Bloomberg Data in Swap Curve Builder (ICSV)
# Incoherence in Bloomberg Data in Swap Curve Builder (ICSV)
When working on calibration for LMM model, we need to have Initial Libor quotes and Swaptions Black vol quotes on the market data. We have data provided by Bloomberg. However, before performing the calibration, we wish to check the coherence of the market data, e.i if we use the right Libor/Discount Rate for the swaption volatility cube (VCUB).
The problems is i can not have the coherence of these data. The ATM swaps has the strike which is the swap rate interest at the present moment. The swap rate is calculable directly from the Libor quotes (deduced from the Discount Rate).
$$ L(t,T_i,T_{i+1}) = \frac{1}{T_{i+1}-T_{i}}(\frac{P(t,T_{i})}{P(t,T_{i+1})} - 1) $$
In the SWPM tab of bloomberg, they said they build swaption VCUB data from EUR 45, which have built data yield curve, zero rate, forward rate ... for calculating swap/swaptions values.
I firstly used these Interest rate curve and recompute swap rate by myselft, I can not reproduce the ATM strike quoted on ATM swap strike matrix.
I secondly use the quoted zero rate curve to recompute the discount curve, $$ P(t,T_i) = \frac{1}{1+r_i T_i} $$ Same thing, i can not reproduce the same values as Bloomberg quotes.
However, these values computed and quoted are approximative equal (relative error around 1% max). So i thing that could be due to the difference of day count, or somethings else. Ideally, i hope check every data are perfectly coherent with theoretical formulas, in the way that the calibration result is not biased due to any kind of these error.
My first question is so does somebody has the idea of why that happens like that, is this normal? How to fixed these data coherence. (Error might come from my computations)
My second question is : is this a big issu if we perform a volatility calibration with these incoherence exist in our data?
Many thanks
## Answer by experquisite (score 1)
https://quant.stackexchange.com/a/14664
It is not normal, for swaptions, your prices should be perfect or you open yourself up to arbitrage. Is Bloomberg calculating the swaptions with dual-curve stripping/bootstrapping? SWDF DFLT has a setting for that. If you are assuming in your model that your discount curve is the same as your forward rates curve, but Bloomberg is doing proper post-2006 OIS discounting, that could explain the discrepancy.
If you cannot replicate the swaptions prices and you are using this model for any sort of real hedging, you are setting yourself up for trouble.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.