Pricing Non-ATM Swaptions from an ATM Volatility Surface

Summary

The document describes how a swaption trader can move from an at-the-money implied volatility surface to prices for options struck away from the money. The answer says that desk models commonly add parameters for the volatility smile and skew: these capture how implied volatility varies with strike, including differences between out-of-the-money and in-the-money options. A SABR-style model is suggested as a framework for representing that behavior.

In practice, the model is calibrated using prices for liquid strikes, after which volatility at other strikes can be inferred and used for pricing. The answer gives a high payer swaption as an example of a liquid calibration point. It also notes that caps tend to be less liquid than swaptions and therefore are not generally the primary instruments for calibrating swaption volatility. This is a concise overview rather than a full workflow: it does not specify model parameters, calibration objectives, quote conventions, or how to validate extrapolated prices.

Key ideas

• An ATM volatility surface alone does not specify volatility at every strike.
• Smile and skew parameters describe how implied volatility changes across option strikes.
• A model such as SABR can be calibrated to liquid market prices and used to infer volatility at other strikes.
• Swaption prices are described as more liquid calibration inputs than cap prices.

Tags

# Swaption Trading


# Swaption Trading












In most Banks, the Traders are provided with ATM Implied vols across different Swaption Expiry's and different Underlying Swap Maturities.(The ATM Implied Vol Cube)

If the trader wants to trade an OTM or ITM Swaption, how would he actually go about pricing the Trade with the ATM Vol Surface he has been provided along with the different analytical tools he will have at his disposal?

## Answer by dm63 (score 6, accepted)

https://quant.stackexchange.com/a/31228

At most banks, swaption traders have models that allow non atm volatilities to be controlled by two parameters. Specifically , a parameter to control the smile (richness of out of the money options) and the skew (whether implied vol is upward or downward sloping as a function of strike ). Look up papers on the SABR model.

In practice, one would calibrate such s model using market prices that are liquid (such as 100bp high payer swaption for example. ). Other strikes could then be inferred from the model.

Just FYI cap prices are less liquid than swaption prices , so they are not specifically used to calibrate swaption vols.

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