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

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  • Useong Shin

Abstract

Put-call parity is a terminal-payoff identity, but its enforcement is capital-using. I study the carry gap, the annualized wedge between option-implied and OIS discount factors, in SPX and RUT index options. Quoted parity is tightly compressed, while the synthetic-traded forward channel leaves a systematic wedge. I interpret this wedge as an implementation premium under finite arbitrage capital. A drift-preserving GBM term, r {\mu}-hat {\tau}, improves in-sample and leave-one-year-out fit, especially in SPX. The evidence suggests that physical drift enters not option payoffs, but the process enforcing risk-neutral parity.

Suggested Citation

  • Useong Shin, 2026. "The P behind Q: Empirical Evidence from Physical Drift in Put-Call Parity," Papers 2605.12250, arXiv.org, revised May 2026.
    • Handle: RePEc:arx:papers:2605.12250
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