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Estimating Unobservable Correlation for Option Valuation

Article Quant Q&A · Author: Arshdeep
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Summary

The note considers how to mark correlation between two equities when there is no directly observable market quote, in the context of pricing an option whose value depends on that relationship. One proposed approach is to identify comparable equity pairs with known correlations and use fundamental ratios to explain differences between pairs, then apply that relationship to estimate the unquoted pair’s correlation. This is presented as an analogy to predicted beta methods.

Another answer clarifies that historical correlation is a measure of realised correlation over the historical sample, but it may differ from future realised correlation. When no implied correlation market exists, the suggested approach is to make a conservative, informed estimate of future correlation, drawing on historical analysis, a market view, or an implied proxy. The note offers alternative sources for an estimate, not a calibrated model or a universal marking rule. The appropriate proxy and conservatism depend on the specific assets and valuation purpose.

Key ideas

  • Comparable equity pairs and their fundamentals can help estimate an unquoted correlation.
  • Historical correlation measures past realised co-movement but does not fix future correlation.
  • Without an implied correlation quote, an estimate may combine historical evidence, market views, and proxies.
  • Correlation assumptions should reflect uncertainty in pricing options that depend on co-movement.

Tags

OptionsDerivatives pricingStatistics
Full text
# What to do if certain parameters are not market observable?


# What to do if certain parameters are not market observable?












Lets say I have no clue on correlation between 2 equities in the market (i.e. i don't have an observable market price). What is the best way to go about marking this correlation for lets say the best of option? One alternative is historical data but that's not the same as realised correlation. Should I mark it conservatively? Use some proxy?

## Answer by Dimitri Vulis (score 1)

https://quant.stackexchange.com/a/53790

If I know some relevant fundamental ratios for these two equities, I might take inspiration from MSCI's predicted beta, which to me means that I would look for other equity pairs whose correlations I know, and see if their fundamentals ratios explain their correlations, and predict what my pairs correlation might be.

## Answer by Soumirai (score 0)

https://quant.stackexchange.com/a/60751

What do you mean by "historical data is not the same as realized correlation"? If you compute historical correlation, it will be the historical realised correlation. Of course it will probably differ from future realized correlation. But if there was some implied correlation market there would be no reason for implied to be in line with future realized as well. It's just market expectation. Now if there is no implied market on this correlation, just like if you try to price an option on an underlier without an implied vol market, you would use some reasonably conservative (because you still want to win the trade) educated guess on what the future realized correlation will be. This guess can be based on historical analysis, a view on the future, an implied proxy, etc...

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