9A.3 OI build-up in options · M09A Options desk

Motivation

Indian commentary labels every strike every day with one of four phrases: long build-up, short build-up, short covering, long unwinding. M07 · 7.5 defined these for futures, proved the OI accounting identity ( $\Delta\text{OI}=N_{oo}-N_{cc}$ , volume $\ge|\Delta\text{OI}|$ ), and listed five reasons the labels are weak evidence. Options add a sixth and seventh reason, both mathematical.

Setup

For an option with price $V(S,t,\sigma)$ , the labels use the sign of the daily change $\Delta V$ and the sign of $\Delta\text{OI}$ : $(+,+)$ long build-up, $(-,+)$ short build-up (on puts often called "put writing"), $(+,-)$ short covering, $(-,-)$ long unwinding.

9A.3.1Decomposing the price change#

Proposition 9A.1what the price change of an option measures

Over one day $\Delta t$ , with spot change $\Delta S$ and implied-vol change $\Delta\sigma$ ,

\Delta V = \Delta\,\Delta S + \tfrac12\Gamma\,(\Delta S)^2 + \Theta\,\Delta t + \mathcal V\,\Delta\sigma + R, \tag{9A.2}

where $R$ collects third-order and cross terms ( $\tfrac16 V_{SSS}\Delta S^3$ , $V_{S\sigma}\Delta S\Delta\sigma$ , ...).

Proof

Taylor's theorem for $V(S,t,\sigma)$ , which is smooth for $\tau>0$ , around $(S,t,\sigma)$ .∎

So the sign of $\Delta V$ is the sign of a sum. For a call it is mostly the sign of $\Delta S$ when $|\Delta\,\Delta S|$ dominates $|\Theta|\Delta t$ , but over a weekend, close to expiry, $\Theta\Delta t$ is large and negative for every option. Then calls and puts can both fall on the same day, and the label for a call reads "bearish" on a day the market rose. A label that depends on the calendar and on the strike's moneyness is not a statement about trader intentions.

9A.3.2Four labels on one day#

Worked example 9A.226 Oct 2026, from the table of 9A.1

The index rose 0.68% over the weekend (23 to 26 Oct, three calendar days with one day of life left afterwards).

Puts at every strike shown fell sharply: the 22,600 put from 150.70 to 38.35, while its OI rose by 81 lakh units. Label: short build-up ("put writers at 22,600"). The fall combines delta (spot up), three days of theta on a four-day option, and a fall in IV.
The 22,750 call rose from 66.45 to 103.55 and OI rose: long build-up. The 22,900 call rose from 33.90 to 39.90 with OI up: long build-up. The 23,000 call fell from 22.20 to 20.05 with OI down: long unwinding, on a day the index rose. Theta over the weekend outweighed delta for this OTM call.
The 22,500 call rose from 175.80 to 292.85 with OI falling by 37 lakh units: short covering.

All four labels appear on one day in one expiry. The reading "put writers are confident, support at 22,600" is the same accounting fact as "put buyers opened 81 lakh units of new longs at 22,600" (M07 · 7.5, reason 1).

9A.3.3Weak evidence and honest tests#

Two more reasons the labels are weak for options

Moneyness and delta. A contract of a deep OTM option has a delta near zero; one of an ITM option has a delta near one. Summing OI across strikes (as "total call OI") adds positions whose exposures differ by two orders of magnitude. SEBI moved index-derivative position limits to delta-based futures-equivalent OI in 2025 for this reason (SEBI circular of 29 May 2025, as reported; M07 · 7.5).
Hedged positions. A large share of option OI belongs to spreads, straddles and hedges of futures or cash. A short call that is half of a call spread is not a bearish view. End-of-day files cannot link legs.

How to test a label honestly Treat each label as a signal $s_t$ observed at the close of day $t$ and test whether it predicts $R_{t,t+h}$ (M04 Definition 4.2). Use non-overlapping horizons or Newey–West errors (M04 Proposition 4.4); cluster by date because all strikes of one day share the same market move; count every label, strike filter and horizon you try (M04 · 4.6). The test in the exercises checks only the classification; the predictive test is Problem 9A.16's pattern applied to labels.

See it live: an F&O stock's page on OI Charts (e.g. https://oicharts.com/stocks/HDFCBANK) shows option OI by strike and futures OI by expiry. Before you read a build-up label off it, apply reasons 6 and 7: which strikes carry the OI, and how much of it is likely to be one leg of a spread?