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A Wiener Chaos Approach to Martingale Modelling and Implied Volatility Calibration

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  • Pere Diaz-Lozano
  • Thomas K. Kloster

Abstract

Calibration to a surface of option prices requires specifying a suitably flexible martingale model for the discounted asset price under a risk-neutral measure. Assuming Brownian noise and mean-square integrability, we construct an over-parameterized model based on the martingale representation theorem. In particular, we approximate the terminal value of the martingale via a truncated Wiener--chaos expansion and recover the intermediate dynamics by computing the corresponding conditional expectations. Using the Hermite-polynomial formulation of the Wiener chaos, we obtain easily implementable expressions that enable fast calibration to a target implied-volatility surface. We illustrate the flexibility and expressive power of the resulting model through numerical experiments on both simulated and real market data.

Suggested Citation

  • Pere Diaz-Lozano & Thomas K. Kloster, 2026. "A Wiener Chaos Approach to Martingale Modelling and Implied Volatility Calibration," Papers 2602.16232, arXiv.org.
    • Handle: RePEc:arx:papers:2602.16232
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    File URL: http://arxiv.org/pdf/2602.16232
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