Comparing Swap-Rate Volatility and Swaption Implied Volatility

Summary

The document poses a research question about estimating an illiquid currency’s swaption volatility surface from hourly observations of more liquid currencies. It asks whether realized volatility measures computed from swap-rate histories can help explain corresponding at-the-money swaption implied volatility, and how to define comparable instruments across currencies. The author describes an exploratory comparison for matching tenor and maturity pairs, including EUR and CHF examples.

The proposed investigation computes exponentially weighted rolling historical volatility for each swap-rate series, then compares the time-varying correlation between those historical-volatility series with the correlation between implied-volatility series. The author reports plotting these quantities for visual inspection, but provides no results or answer establishing that they are similar or predictive. The central limitation is that correlation is offered as an initial notion of similarity, without a validation design, statistical test, or method for constructing the target surface. The text is useful as a research framing and a preliminary workflow, rather than as a demonstrated volatility-mapping method.

Key ideas

• The research goal is to infer illiquid swaption volatility information from more liquid markets.
• Matching swap-rate tenors and maturities is one proposed basis for comparing instruments across currencies.
• The author compares exponentially weighted historical volatility and implied-volatility correlation series.
• Visual inspection is exploratory and does not establish predictive usefulness or statistical significance.
• The document does not provide a completed volatility surface estimation method.

Tags

# Metric for volatility time series similarity - European swaptions


# Metric for volatility time series similarity - European swaptions












I'm trying to estimate the volatility surface of illiquid swaptions (say CHF) given hourly data (atm vol, skew, for different strikes) of other liquid swaptions (EUR, USD, etc.). Having the underlying swap rates time series available for all ccys, I would also like to know if some vol measure computed on, e.g. EUR-1M-5Y swap rate, is informative on the corresponding swaption ATM vol. From the little information I've found around, I would try to proceed as outlined in this answer (volatility mapping section) where the main difficulty for me is defining what a "similar asset" with respect to my goal. Since I don't know what to do, I took "similar" = "correlated" hence if we consider for example the 1M-5Y EUR and CHF swaption/swaprates, I did the following:

- Compute the exponentially weighted rolling Historical Volatility (HV) for both 1M-5Y swaprate series.

- Compute the exponentially weighted correlation between the two HV time series (say Rhv(t))

- Compute the exponentially weighted correlation between the two Implied Volatility (IV) time series (say Riv(t))

- Is Rhv(t) similar to Riv(t) ? Here I'm just plotting hence visual inspection as I don't know what is the proper thing to do (if any).

Does this make vaguely sense for those of you that have some more experience in this kind of time-series analysis? I have mostly been reading Brian B and Lehalle users amazing answers but apparently I need some more help.

Many thanks to you all!

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