Assessing Swaption Volatility and Risk for Out-of-the-Money Trades

Summary

The document raises a risk-estimation question for out-of-the-money swaptions in a low or negative interest-rate setting. The author proposes using the Bachelier model with implied volatilities, then finds a very large annualized volatility for a long-dated EUR swaption struck away from the money and asks whether that estimate is plausible.

Two possible approximations are considered: a delta-normal approach that scales rate volatility by option sensitivity and a duration-based scaling. The author asks which underlying rate should be used and whether comparable figures can be found in market data or risk software. No answer, supporting evidence, or recommended calibration method is included, so the document frames the problem without resolving it. Its useful contribution is to highlight that swaption risk depends on the chosen rate exposure and on translating rate volatility into option-value volatility; the proposed approximations remain unvalidated here.

Key ideas

• The author uses a Bachelier framework to handle swaptions when rates may be negative.
• A large implied volatility estimate for an out-of-the-money swaption motivates the risk question.
• The document considers delta-normal and duration-based ways to relate rate volatility to option risk.
• It does not specify which rate to use or provide a validated estimate or answer.

Tags

# Estimate the risk of swaptions


# Estimate the risk of swaptions












I would like to model OTM Swaptions. I can use some implementation of the Bachelier model (not B76 due to negative rates) and implied volatilities from Bloomberg.

For 10Y X 10Y (10 years option maturity, 10 years swap length) and 100 bps OTM I get something like 100% volatility pa for the EUR.

I would like to make this number plausible. Does it make sense to use a delta normal method here? Thus apply $$ \sigma \approx \Delta \times \text{vola(rate}) \times f $$ where $f$ should be some leverage factor. Which rate would I use? What if I look at duration and put $$ \sigma \approx D \times \text{vola(rate}), $$ again which rate?

Are there comparable numbers on the web or in Bloomberg? I can not estimate the volatility of swaptions in PORT, right?

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