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

Battle Count: 72

The paper is highly relevant to options arbitrage desks and quantitative risk managers who enforce put-call parity. It provides a state-dependent framework for understanding why parity residuals persist in carry space even when price-space residuals are compressed. The fitted carry gap can serve as a price-space implementation hurdle for evaluating whether a parity residual is large enough to compensate for enforcement costs. However, it is not a direct trading signal or forecasting model; it is a reduced-form diagnostic of implementation costs. The results are most relevant for index options (SPX, RUT) and the synthetic-forward/futures channel.

The core regression is straightforward OLS with HAC inference. However, the carry-gap construction requires: (1) minute-level option NBBO data, (2) cross-sectional synthetic-forward identification (Azzone-Baviera procedure), (3) OIS curve bootstrapping, (4) rolling OLS drift proxy with look-ahead-bias prevention, and (5) careful sample filtering. The theoretical derivation of GBM terms is accessible but requires comfort with Brownian motion running maxima. LOYO validation adds computational overhead. Access to proprietary data (ThetaData, Databento, OIS curves) is the main practical barrier.

The paper provides detailed descriptions of the carry-gap construction pipeline (Azzone and Baviera 2021 synthetic-forward identification), OIS bootstrapping, rolling OLS drift proxy, and regression specifications. Data sources are named (ThetaData for option NBBO, Databento for futures BBO, FRED for NFCI, OIS data from Michele Azzone). However, no code repository is provided, and some data (OIS curve, ThetaData) require paid access. The 504-day lookback and HAC(21) choices are clearly stated. Reproduction would require access to proprietary option and OIS data.