Building a Yield Curve and Selecting Swaption Volatility Inputs

Summary

The document addresses two inputs needed when calibrating a swaption model with QuantLib: the volatility convention and the interest-rate term structure. It notes that QuantLib’s cited calibration example expects Black, or lognormal, volatilities by default, and gives an approximate volatility from that example. This helps distinguish Black volatility from normal volatility quotes, whose numerical levels can differ substantially.

For the curve, the example uses a flat forward rate to create a yield-curve object. An alternative is to build the curve from market instruments such as deposits, forward-rate agreements, and swaps, then bootstrap discount factors and rates. The answer points to examples and a cookbook for implementation details, but does not explain interpolation choices or how to load a full set of market discount factors and zero rates. Users therefore need to confirm quote conventions and choose appropriate curve construction and interpolation methods for their market data.

Key ideas

• The cited QuantLib calibration example uses Black lognormal swaption volatilities by default.
• Black and normal volatility quotes use different conventions and may have different numerical scales.
• A flat forward curve is one way to initialize the yield term structure.
• Market deposits, forward-rate agreements, and swaps can be used to bootstrap a curve.
• The answer does not specify detailed interpolation or market-data handling procedures.

Tags

# Constructing Daily Term Structure


# Constructing Daily Term Structure












I am very new to QuantLib and am trying to do Swaption Model calibration following the example here:http://gouthamanbalaraman.com/blog/short-interest-rate-model-calibration-quantlib.html

Appreciate if someone could help me with the following question:

- what is model behind the implied volatility data as the input for calibration? On bloomberg there are black model and normal model. I am thinking is black model as the vol for normal model is generally much smaller.

- How to feed in the term structure from the market and do the interpolation? Using Bloomberg I can get the discount factors and the zero rate for 1 week up to 50 years. How should I provide this data into the YieldTermStructureHandle function to construct my term structure?

## Answer by David Duarte (score 1)

https://quant.stackexchange.com/a/50475

- You are correct. By default QuantLib expects black vols (lognormal). In the example you sent, that would be approx. 11%.

- In that example, a flat forward rate is being used to build a curve object. Alternatively, you can feed market instruments (deposites, fras, swaps) to bootstrap a curve. You can check out a simple example in the post link or check out the excelent QuantLib cookbook for examples of building curves

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.