CMS: covering all bases

Simon Cedervall and Vladimir Piterbarg develop a new vanilla model that directly links constant maturity swap (CMS) and payment convexity in general payouts to volatilities of swaptions of all relevant tenors, as well as prices of CMS spread options, while carefully controlling for potential sources of arbitrage. The model also accounts for the stochastic Libor-overnight indexed swap basis

Constant maturity swap (CMS) convexity adjustments are driven by the covariance between the underlying swap rate, its associated annuity and the discount bond of the payment delay. This implicitly involves the volatility and correlations of rates of different tenors, and since there is a developed derivatives market in all these quantities (via caps, swaptions and CMS spread options, for instance), the size of the convexity adjustment can be linked to market-implied volatilities and correlations