Paper: arXiv 2605.02040

Authors: Elisa Alòs, Òscar Burés

Abstract

It is well-known that, in the Bachelier model, when asset prices and volatilities are uncorrelated, the implied volatility coincides with the fair value of the volatility swap. In this paper, via classical Itô calculus and Taylor expansions, we write the price for out-of-the-money (OTM) and in-the-money (ITM) options as an expansion with respect to the moneyness, where the coefficients are related to the negative (non-integer) powers of the future mean volatility. As an a application, we use it as a control variate to reduce the variance of Monte Carlo option prices in the correlated case.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 4.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper relies heavily on rigorous Itô calculus, Taylor expansions, and formal proof derivations, placing it high on mathematical complexity. While it discusses an application as a control variate for Monte Carlo, the empirical section is primarily illustrative/supportive of the theory rather than being a comprehensive, data-heavy backtesting implementation.

Research Flowchart

  flowchart TD
    A[Research Goal: Analytic approximation for Bachelier option prices] --> B[Methodology: Itô calculus & Taylor expansions]
    C[Inputs: Asset price & volatility model] --> B
    B --> D[Process: Expansion w.r.t moneyness]
    D --> E[Outcome: Negative power volatility coefficients]
    E --> F[Application: Control variate for Monte Carlo]
    F --> G[Result: Reduced variance in correlated cases]

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2 of 38 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.