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Watanabe's expansion: a solution for the convexity conundrum

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  • D. Garcia-Lorite
  • R. Merino

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.

Suggested Citation

  • D. Garcia-Lorite & R. Merino, 2025. "Watanabe's expansion: a solution for the convexity conundrum," Quantitative Finance, Taylor & Francis Journals, vol. 25(5), pages 711-732, May.
    • Handle: RePEc:taf:quantf:v:25:y:2025:i:5:p:711-732
    DOI: 10.1080/14697688.2025.2491691
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