# 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 ?

## 1 Answer

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.

• Oh ok. I am trying to do the converse : backing out the correlation to use it for a pricing of a mid-curve swaption whose payoff I approximated (by freezing some annuities fractions to their time-0 value) by a "generalized" spread option, of pay-off $\max(\alpha S_T^1 - \beta S_T^2,0)$ where the $S_T^i$ are the two CMS rates. – ujsgeyrr1f0d0d0r0h1h0j0j_juj May 14 '18 at 6:47
• Actually I know that many banks quick price mid-term swaption like this, with a gaussian copula, backing out its $\rho$ from the aforementioned correlation. – ujsgeyrr1f0d0d0r0h1h0j0j_juj May 14 '18 at 7:26