  In this paper, we present a new method for pricing CMS derivatives. We use
Mallaivin's calculus to establish a model-free connection between the price of
a CMS derivative and a quadratic payoff. Then, we apply Watanabe's expansions
to quadratic payoffs case under local and stochastic local volatility. Our
approximations are generic. To evaluate their accuracy, we will compare the
approximations numerically under the normal SABR model against the market
standards: Hagan's approximation, and a Monte Carlo simulation.
