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

TL;DR

This paper investigates the physical drift in put-call parity, revealing a systematic wedge caused by finite arbitrage capital, and introduces a drift-preserving model that improves fit to market data.

Contribution

It provides empirical evidence of physical drift affecting put-call parity enforcement and proposes a model incorporating this drift for better market fit.

Findings

Quoted parity is tightly compressed.

A systematic wedge exists due to finite arbitrage capital.

A drift-preserving GBM model improves fit, especially in SPX.

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.