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arXiv · 2605.12250

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

Useong Shin
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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.

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Useong Shin. 2026-05-12. The P behind Q: Empirical Evidence from Physical Drift in Put-Call Parity. https://arxiv.org/abs/2605.12250

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