Interest rate convexity and the volatility smile

When pricing the convexity effect in irregular interest rate derivatives such as, e.g., Libor-in-arrears or CMS, one often ignores the volatility smile, which is quite pronounced in the interest rate options market. This note solves the problem of convexity by replicating the irregular interest flow or option with liquidly traded options with different strikes thereby taking into account the volatility smile. This idea is known among practitioners for pricing CMS caps. We approach the problem on a more general scale and apply the result to various examples.