Watanabe's expansion: a solution for the convexity conundrum

D. Garcia-Lorite and R. Merino

Quantitative Finance, 2025, vol. 25, issue 5, 711-732

Abstract: 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.

Date: 2025
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DOI: 10.1080/14697688.2025.2491691

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