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Estimating Swap-Rate Correlation Without Spread Options

Article Quant Q&A · Author: sigma1988
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Summary

The document asks how to estimate correlation between swap rates when spread options are unavailable. One proposed approach is to infer correlations among forward rates from cap and floor prices and swaption volatility surfaces, then use the relationship between forwards and swap rates to estimate swap-rate correlation.

The response cautions that the pricing difference between caps and floors and swaptions depends on both correlation and the volatility term structure, so it cannot be interpreted as a clean correlation measure. It suggests estimating historical correlations across multiple observation windows and using a long-run average as a simpler alternative. This is a short answer rather than a fully specified estimation procedure: it gives no data requirements, window lengths, model assumptions, or comparison of historical estimates with market-implied measures. Its central lesson is that volatility structure can confound attempts to back out correlation from option prices.

Key ideas

  • A cap and swaption pricing difference reflects volatility term structure as well as correlation.
  • That pricing difference is therefore not a pure measure of swap-rate correlation.
  • Historical correlations over several observation windows offer a direct estimation alternative.
  • A long-run average can summarize historical estimates, though the document does not specify a window or model.

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Fixed incomeOptionsStatistics
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# Estimate swap rates correlation in absence of spread options


# Estimate swap rates correlation in absence of spread options












Any suggestions / pointers on how to estimate swap rates correlation in absence of spread options? Is it feasible to work it out with the correlation of forwards coming from the intersection of capfloors and swaption prices/volatility surfaces and then deduce the correlation of swap rates given the relationship between forwards and swap rates?

## Answer by dm63 (score 2)

https://quant.stackexchange.com/a/81130

Your suggested procedure doesn’t work very well. The ‘wedge’ between cap/floors and swaptions depends on the volatility term structure as well as correlation, so it is not a pure measure.

I believe it is simplest just to measure historical correlations over various observation windows and estimate the long term average.

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