Paper: arXiv 2601.14852

Authors: Tjeerd De Vries

Abstract

We propose a projection method to estimate risk-neutral moments from option prices. We derive a finite-sample bound implying that the projection estimator attains (up to a constant) the smallest pricing error within the span of traded option payoffs. This finite-sample optimality is not available for the widely used Carr–Madan approximation. Simulations show sizable accuracy gains for key quantities such as VIX and SVIX. We then extend the framework to multiple underlyings, deriving necessary and sufficient conditions under which simple options complete the market in higher dimensions, and providing estimators for joint moments. In our empirical application, we recover risk-neutral correlations and joint tail risk from FX options alone, addressing a longstanding measurement problem raised by Ross (1976). Our joint tail-risk measure predicts future joint currency crashes and identifies periods in which currency portfolios are particularly useful for hedging.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 8.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a rigorous mathematical framework using a projection approach that outperforms the canonical Carr-Madan formula, complete with finite-sample error bounds and theoretical proofs. Its empirical application to FX options successfully solves a long-standing measurement problem regarding joint risk-neutral distributions and crash prediction with strong econometric validity.

Research Flowchart

  flowchart TD
    A[Goal: Improve Risk-Neutral Moment Estimation & Joint FX Risk] --> B[Inputs: Traded Option Prices - Single & Multi-Asset FX]
    B --> C[Projection Method: Map Target Payoffs to Traded Span]
    C --> D[Derive Finite-Sample Bounds & Completeness Conditions]
    D --> E[Estimate Risk-Neutral Moments, Correlations & Joint Tail Risk]
    E --> F[Findings: Outperforms Carr-Madan VIX/SVIX & Predicts Currency Crashes]

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0 of 152 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.