Pricing convexity adjustment with Wiener chaos

This paper presents an approximated formula of the convexity adjustment of Constant Maturity Swap rates, using Wiener Chaos expansion, for multi-factor lognormal zero coupon models. We derive closed formulae for CMS bond and swap and apply results to various well-known one-factor models (Ho and Lee (1986), Amin and Jarrow(1992), Hull and White (1990), Mercurio and Moraleda (1996)). Quasi Monte Carlo simulations confirm the efficiency of the approximation. Its precision relies on the importance of second and higher order terms.