How CMS Spread Options Are Quoted and Valued

Summary

The document describes a market quotation for a one-year at-the-money straddle on the difference between the ten-year and two-year constant maturity swap rates. The quoted bid and offer are given as prices in percentage terms, rather than as an implied normal or lognormal volatility. The example clarifies that the market quote refers to the option premium on the CMS spread.

For valuation, the response says traders commonly use volatilities from swaptions on the relevant forward rates together with their correlation. These inputs produce a normalized volatility for the spread, which is then used to calculate the option value. This outlines a way to connect rate-option market inputs to a spread option, but does not specify the exact model, volatility conventions, calibration, or numerical valuation steps. The example is a broker quote and does not establish that all markets or counterparties use the same quoting practice.

Key ideas

• The example CMS spread straddle is quoted by its price rather than implied volatility.
• The spread is the difference between the ten-year and two-year CMS rates.
• Swaption volatilities on the component forward rates and their correlation can inform spread volatility.
• The resulting normalized spread volatility is used to value the option.
• The document does not specify a full model or universal market convention.

Tags

# CMS spread vanilla options quotation


# CMS spread vanilla options quotation












How are vanilla (call/put) options on CMS spread quoted on the markets ? Through an implied (normal/lognormal) volatility with a normal/lognormal model on the spread in the forward measure ?

## Answer by dm63 (score 2)

https://quant.stackexchange.com/a/39771

Here is a quotation from an interbank broker last week: 1Y 2-10 Str 26-27. This means that a one year at the money straddle on the (10yr cms - 2 yr cms) has a spot price of 0.26% bid, 0.27% offered. So, they are quoted in price terms , not volatility.

To value the above option, most traders would use the volatility of 1y-2y and 1y-10y swaptions , and a correlation between those forward rates. This produces a normalized volatility for the spread, which is then used to compute the value.

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