The P behind Q: Empirical Evidence from Physical Drift in Put-Call Parity

Paper: arXiv 2605.12250

Authors: Useong Shin

Abstract

Put-call parity is exact as a terminal-payoff identity, yet its market enforcement is path-dependent and capital-using. This paper examines whether physical-measure drift is reflected in the carry gap, defined as the annualized wedge between option-implied and OIS-implied discounting, using SPX and RUT European index options. I derive a drift-preserving extension of the GBM implementation-risk term that adds an (rμτ) component to the standard (rσ\sqrtτ) path-risk component. The drift input (μ) is measured by a lagged rolling-OLS trend proxy and should not be interpreted as an observed expected return. Empirically, the drift term improves both in-sample and leave-one-year-out fit, especially for SPX, consistent with drift-sensitive margin burden in parity enforcement rather than a failure of no-arbitrage.

Complexity vs Empirical Score

• Math Complexity: 6.5/10
• Empirical Rigor: 7.5/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a solid theoretical extension of the implementation-risk term in put-call parity by incorporating physical drift, backed by robust out-of-sample empirical testing on SPX and RUT index options. The findings offer practical insights into margin burdens and carry gaps without claiming no-arbitrage failures.

Research Flowchart

  flowchart TD
    A[Research Goal: Assess if physical drift μ affects Put-Call Parity carry gap] --> B[Data Inputs: SPX & RUT Options, OIS Rates, Lagged Rolling-OLS μ]
    B --> C[Derive Extended Model: Add drift-risk component rμτ to standard rσ√τ implementation risk]
    C --> D[Empirical Valuation: In-Sample & Leave-One-Year-Out Fit Testing]
    D --> E[Outcome: Drift term improves fit, confirming drift-sensitive margin burden in parity enforcement]