Copula Pricing of CMS Spread Options and the Limits of Skew

Summary

The document describes a practical copula-based approach for pricing constant-maturity-swap spread options. The inputs are the basis-point volatilities of the two rates and a correlation estimate. In the described workflow, these inputs are used to fit the at-the-money option, with a skew adjustment applied when pricing out-of-the-money strikes.

The account reports that this method can approximate at-the-money market prices when the volatilities come from relevant swaption implied volatilities and the correlation reflects recent realized co-movement. It also states that the approach often undervalues out-of-the-money options because it does not capture the market’s significant skew. The discussion does not provide quantitative error measures or separate evidence for short expiries, so it cannot establish accuracy for options expiring within six months. Calibration quality and treatment of skew remain central limitations.

Key ideas

• The described copula method uses two rate volatilities and a correlation input.
• Relevant swaption implied volatilities and recent realized correlation are suggested inputs for at-the-money calibration.
• The method is reported to approximate at-the-money market prices reasonably when appropriately calibrated.
• Out-of-the-money prices may be underestimated because the basic procedure does not capture significant skew.
• The document provides no quantitative evidence specifically establishing accuracy for short-expiry options.

Tags

# What are the pros/cons of using a copula model to price CMS spread options, in particular ones with short expiries?


# What are the pros/cons of using a copula model to price CMS spread options, in particular ones with short expiries?












The expiry of the option may not be relevant to the question, but I would be curious to know if a copula model would provide an accurate price for sub 6 month expiry options.

## Answer by dm63 (score 1)

https://quant.stackexchange.com/a/76651

A copula model for CMS spread options takes as inputs the basis point volatility of each rate and a correlation coefficient. Typically these are used to calibrate the ATM option, and then a skew is applied for OTM options.

As to whether this is ‘accurate’, what does this mean ? In my experience, this procedure approximates reasonably closely the market price of ATM options, assuming the 2 vols are the implied vols of the appropriate swaptions and the correlation input is the recent realized correlation between the 2 rates. However for OTM options typically the procedure underestimates the market price because there is usually a significant skew.

Hence the copula model can be said to be a reasonable pricing methodology, appropriately calibrated, but the fact it doesn’t capture skew means that it is not a very sophisticated approach.

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