Option Liquidity Scoring

How SOPHIE's per-contract liquidity score works: why spread gates the score multiplicatively rather than being outvoted by open interest, the log-scaled volume/OI components, and how a contract with a wide unfillable quote can never be rescued by size.

Overview

Implementation spec for the per-contract liquidity score in SOPHIE's options chain (OptionsMatrixTable, lib/options/liquidity.ts). The score answers one practical question: if I send this order, will it fill at a price close to the mid?

It is calibrated specifically to SPX microstructure, where ATM spreads trade extremely tight (under 0.3%) and widen rapidly out-of-the-money. A generic equity-options model mis-scores SPX badly in both directions.

Mid Price and Spread

\text{Mid Price} = \frac{\text{Bid} + \text{Ask}}{2}, \qquad \text{Spread \%} = \frac{\text{Ask} - \text{Bid}}{\text{Mid Price}}

Design Principle: Spread Gates the Score

The central modelling decision. A contract with enormous open interest but an unfillable quote — say $0.00 bid against a$ 5.00 ask — is not liquid, however much size rests there.

So spread acts as a strict multiplicative gate, not as one arithmetic component that heavy open interest can outvote. A naive weighted average of spread, volume and OI would rank that contract as tradeable. This model cannot: if the spread score is zero, the composite is zero regardless of activity.

Component Scores

Spread score — a piecewise-linear curve whose breakpoints reflect where SPX quotes actually sit:

\text{Score}_{\text{spread}} = \begin{cases} 100 & \text{Spread \%} \le 0.3\% \\ 100 - 30 \times \frac{\text{Spread \%} - 0.003}{0.010 - 0.003} & 0.3\% < \text{Spread \%} \le 1.0\% \\ 70 - 40 \times \frac{\text{Spread \%} - 0.010}{0.030 - 0.010} & 1.0\% < \text{Spread \%} \le 3.0\% \\ 30 - 30 \times \frac{\text{Spread \%} - 0.030}{0.080 - 0.030} & 3.0\% < \text{Spread \%} \le 8.0\% \\ 0 & \text{Spread \%} > 8.0\% \end{cases}

Volume and open interest scores — both log-scaled, because activity is roughly log-distributed across a chain and a linear scale would let a handful of ATM strikes dominate everything:

\text{Score}_{\text{vol}} = \min\left(100, \frac{\log_{10}(\text{Volume} + 1)}{\log_{10}(1001)} \times 100\right)

\text{Score}_{\text{OI}} = \min\left(100, \frac{\log_{10}(\text{OI} + 1)}{\log_{10}(5001)} \times 100\right)

The different denominators set the saturation points: volume saturates at ~1,000 contracts traded, open interest at ~5,000 resting.

Activity score — volume weighted above open interest, since today's trading is a better signal of a live market than resting size that may be stale:

\text{Score}_{\text{activity}} = 0.65 \times \text{Score}_{\text{vol}} + 0.35 \times \text{Score}_{\text{OI}}

Composite Score

\text{Score}_{\text{composite}} = \text{round}\left( \text{Score}_{\text{spread}} \times \left(0.55 + 0.45 \times \frac{\text{Score}_{\text{activity}}}{100}\right) \right)

The $0.55 + 0.45(\cdot)$ envelope is what makes spread a gate rather than a veto. A tight-spread contract with no activity still scores 55% of its spread score — genuinely tradeable, just quiet. A wide-spread contract cannot be rescued by activity, because the multiplier only ever scales down from the spread ceiling.

Tier	Score	Badge
Excellent	$\ge 75$	Emerald
Good	50–74	Blue
Fair	25–49	Amber
Poor	$< 25$	Rose

How This Kind of Score Is Used in Practice

A composite liquidity score of this shape is a standard building block on professional execution desks, not a SOPHIE-specific idea — it's the same logic behind smart-order-routing and pre-trade "tradability" checks that route flow away from contracts likely to produce poor fills. In practice traders use a score like this three ways:

Screening. Filtering a chain down to strikes actually worth quoting, before looking at price at all — useful on wide chains like SPX where hundreds of strikes are listed but liquidity concentrates near the money.
Sizing. A thin contract that would move on a 1-lot can still be fine for size 1, but the same score should discourage size 50 — spread and depth both matter to how much size a quote can actually absorb, which a pure spread-percentage number doesn't capture.
Execution timing. Spread and volume both vary through the trading day — tightest near the open/close and around major index rebalances, widest in quiet midday stretches — so desks that watch a rolling liquidity score rather than a static one avoid trading into temporarily bad conditions.

Limitations

Quotes are a snapshot. A tight spread at the moment of capture says nothing about depth behind it, or whether the quote survives an order of size.
Volume is same-day, open interest is prior-day. They are measured over different windows, so the activity blend mixes two clocks.
Calibrated to SPX. The breakpoints assume index-option microstructure and would need recalibration for single-name equity options, where 1% spreads can be normal rather than mediocre.

Key Takeaways

Spread gates the score multiplicatively — size never rescues an unfillable quote.
Volume and OI are log-scaled, saturating at ~1,000 and ~5,000 contracts.
Volume is weighted 0.65 against OI's 0.35: live trading beats resting size.
A quiet but tight contract floors at 55% of its spread score rather than collapsing.