Paper: arXiv 2602.16232

Authors: 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.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 7.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents an innovative, mathematically elegant framework using truncated Wiener-chaos expansions to model arbitrage-free martingales for implied volatility calibration. It balances deep functional analysis and Malliavin calculus with practical numerical calibration on both synthetic (Heston, rough Heston) and real SPX market option surfaces.

Research Flowchart

  flowchart TD
    A[Research Goal: Fast & Flexible Calibration to Implied Volatility Surface] --> B[Data Inputs: Target Option Prices & Volatility Surfaces]
    B --> C[Methodology: Truncate Wiener Chaos Expansion at Terminal Value]
    C --> D[Compute Conditional Expectations via Hermite Polynomials]
    D --> E[Calibration: Fit Over-Parameterized Martingale Model to Market Data]
    E --> F[Outcomes: Expressive Martingale Model & Rapid Calibration Strategy]

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1 of 42 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.