Watanabe's expansion: a solution for the convexity conundrum
提出一种基于Malliavin微积分和Watanabe展开的新方法，用于定价CMS衍生品，在局部和随机局部波动率模型下给出通用近似，并通过数值比较验证精度。
In this paper, we introduce a new method for pricing CMS derivatives. We utilize Malliavin'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 under local and stochastic local volatility. The local and stochastic local volatility models are expressed in a general form, providing a generic approximation. To evaluate their accuracy, we will compare the approximations numerically under the normal SABR model against the market standards: Hagan's approximation and Monte Carlo simulation.