Watanabe’s expansion: A Solution for the convexity conundrum

ArXiv ID: 2404.01522 “View on arXiv”

Authors: Unknown

Abstract

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.

Keywords: CMS Derivatives, Mallevin Calculus, Watanabe Expansions, Local Volatility, Stochastic Volatility, Derivatives

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 6.5/10
• Quadrant: Holy Grail
• Why: The paper employs advanced mathematical tools like Malliavin calculus and Watanabe expansions to derive approximations for pricing CMS derivatives, demonstrating high mathematical complexity. It includes a backtest-ready validation against Monte Carlo simulations and market-standard models, supported by open-source code, indicating strong empirical rigor.

  flowchart TD
    A["Research Goal:<br>Pricing CMS Derivatives<br>for better accuracy"] --> B["Key Methodology:<br>Watanabe's Expansion"]
    B --> C["Input Data:<br>SABR Model Parameters<br>(Local & Stochastic Vol)"]
    C --> D["Computational Process:<br>Compare Approximations"]
    D --> E["Numerical Results<br>vs Hagan's & Monte Carlo"]
    E --> F["Key Findings:<br>Model-Free Link Established<br>Generic Approximations Validated"]