Stock Market Indexing and Option Market Conditions: Chang, Ge, Lin & Ma (2026)

What this is. The paper’s core results, the measure it constructs (put-call parity deviation as a proxy for option market conditions), and the regression discontinuity design it applies (local linear regressions around the Russell 1000/2000 threshold): enough to know what it found and how, without reading the full paper. To replicate or extend it, read the full source at the original.

TL;DR

Using the annual Russell 1000/2000 Index reconstitution as a regression discontinuity design (following Chang et al. (2015)), the paper finds that stocks at the top of the Russell 2000 Index exhibit better option market conditions than similar-sized stocks at the bottom of the Russell 1000 Index, over 1998-2006. Specifically, indexed stocks have smaller put-call parity deviations, higher options trading volume, and narrower options bid-ask spreads. Boone and White (2015) document that these same threshold stocks have higher stock liquidity and lower information asymmetry. The paper argues the channel is a supply-side liquidity spillover: improved stock liquidity reduces the hedging costs of options market makers, who hedge by trading the underlying stock, making them more willing to provide liquidity in options. The results do not support the lending-fee channel as the primary explanation: call options bid-ask spreads are more affected than put spreads, opposite to the prediction under a short-selling-cost mechanism. The results are consistent with Kamara and Miller (1995), who show that higher options liquidity reduces put-call parity violations.

Core results

Magnitudes as reported; \*\* = 5%, \*\*\* = 1%. Main regressions use local linear regressions around the Russell 1000/2000 threshold, bandwidth ±50 stocks, year and industry fixed effects, 1998-2006. Each row gives its own locator and bandwidth where applicable.

#	Result	Locator	Magnitude
R1	Stocks at top of Russell 2000 have smaller put-call parity deviations (Absoptivspread) than similar-sized stocks at bottom of Russell 1000	Table 2, col. 3, p. 7	Dum2000 = -0.004** (t = -2.42); N = 199
R2	Indexed stocks have higher options trading volume (log total contracts)	Table 3, col. 3, p. 8	Dum2000 = 0.561*** (t = 5.28); N = 368
R3	Indexed stocks have narrower options bid-ask spreads (open-interest-weighted, %)	Table 4, col. 3, p. 9	Dum2000 = -2.781*** (t = -4.59); N = 368
R4	Call bid-ask spreads are more affected than put bid-ask spreads, inconsistent with the lending-fee channel prediction	Tables 5 and 6, pp. 10-11	Volume: put Dum2000 = 0.566*** (t = 4.53), call Dum2000 = 0.524*** (t = 3.53); Spreads: put Dum2000 = -1.731*** (t = -2.80), call Dum2000 = -3.565*** (t = -6.25)
R5	Alternative liquidity measure: indexed stocks have fewer zero trading volume days (OptNZVD)	Table 8, col. 3, p. 13	Dum2000 = -32.774*** (t = -5.68); N = 321
R6	Alternative liquidity measure: indexed stocks have lower options ILLIQ (Optilliq)	Table 9, col. 3, p. 14	Dum2000 = -0.050*** (t = -5.32); N = 303
R7	The cutoff groups have similar median size, while the Russell 2000 group has higher analyst coverage and stock trading volume and lower analyst forecast dispersion	Table 1, p. 6; §3.1, p. 6	Median LNMAYSIZE: 14.37 (Russell 1000) vs 14.14 (Russell 2000); mean analyst count: 9.03 vs 9.78; forecast dispersion: 0.34 vs 0.26; stock volume: 0.53m vs 0.67m
R8	Indexing raises put and call options volume similarly, consistent with the supply-side liquidity channel	Table 5, p. 10	Put: Dum2000 = 0.566*** (t = 4.53); call: Dum2000 = 0.524*** (t = 3.53); N = 316 each
R9	Lower put-call parity deviations persist under narrower and wider bandwidths	Table 7, Panel A, cols. 3 and 6, p. 12	Bandwidth 25: Dum2000 = -0.005** (t = -2.28), N = 101; bandwidth 75: -0.003** (t = -2.10), N = 313
R10	Higher options volume persists under narrower and wider bandwidths	Table 7, Panel B, cols. 3 and 6, p. 12	Bandwidth 25: Dum2000 = 0.514*** (t = 2.83), N = 184; bandwidth 75: 0.339*** (t = 4.54), N = 545
R11	Narrower options bid-ask spreads persist under narrower and wider bandwidths	Table 7, Panel C, cols. 3 and 6, p. 12	Bandwidth 25: Dum2000 = -2.489*** (t = -2.96), N = 184; bandwidth 75: -2.167*** (t = -4.34), N = 545

Overall (paper’s conclusion). The stock market indexing effect, identified via the Russell 1000/2000 reconstitution, improves option market conditions through liquidity spillovers from equity markets to options markets. The supply-side channel, where options market makers face lower hedging costs when underlying stock liquidity improves, dominates the potential demand-side effect; the call-put spread comparison does not support lending fees as the primary explanation. Results are robust to alternative bandwidths (±25 and ±75 stocks, Table 7) and alternative liquidity measures (OptNZVD, Optilliq, Tables 8-9).

Theory / model

The paper has no formal economic model. It tests two empirical hypotheses derived from the stock indexing mechanism.

H1 (option market conditions). If stock market indexing improves stock liquidity and reduces information asymmetry for stocks just above the Russell 1000/2000 threshold (documented by Boone and White (2015)), then put-call parity deviations for options on those stocks should be smaller. The put-call parity deviation reflects demand pressure for call options relative to put options (Cremers and Weinbaum, 2010), and better-informed or more active market making reduces such imbalances (Rösch et al. (2017)).

H2 (supply-side liquidity spillover). Options market makers hedge their positions by trading the underlying stock. When stock liquidity improves, their hedging costs fall, making them more willing to provide options liquidity (wider coverage, narrower spreads). This supply-side shift predicts higher options volume and narrower bid-ask spreads simultaneously.

Mechanism distinction. A demand-side story, where informed arbitrageurs are more attracted to better-liquid stocks and increase options activity, would predict higher volume but wider bid-ask spreads (adverse selection). A lending-fee channel, where lower short-selling costs reduce the replication cost of put options, would predict stronger effects on put options relative to call options. The paper tests these alternatives using separate call and put regressions (Tables 5 and 6): call bid-ask spreads are more affected than put spreads, which does not support the lending-fee channel as the primary explanation and points toward the supply-side market-making mechanism.

Identification. Each year, Russell constructs the Russell 1000 and Russell 2000 indexes based on market capitalization at end of May; portfolio weights are released in June. Stocks just above the cutoff enter the Russell 2000 with high portfolio weights (the 2000 index has a smaller aggregate market cap denominator), while stocks just below enter the Russell 1000 with low portfolio weights. Market capitalizations around the threshold are continuous, but portfolio weights jump discontinuously, providing near-random assignment in a narrow bandwidth. Chang et al. (2015) establish that this generates significant stock price effects. The paper follows the same setting, focusing on stocks within ±50 ranks of the threshold (1998-2006, ending before Russell’s 2007 banding policy change).

Method

The paper follows Lin et al. (2019) and adopts local linear nonparametric regression as the estimator. This avoids the boundary bias that kernel regression (Nadaraya-Watson) produces near the support boundary of the running variable (p. 5). The option market conditions measure follows Rösch et al. (2017): the absolute deviation from put-call parity for stock $i$ on day $t$ is the open-interest-weighted average absolute difference in implied volatilities across matched call-put pairs (equation (1), p. 4):

$$\text{Absoptivspread}_{i,t} = \left| IV_{i,t}^{\text{calls}} - IV_{i,t}^{\text{puts}} \right| = \left| \sum_{j=1}^{N_{i,t}} w_{j,t}^{i} \left( IV_{j,t}^{i,\text{call}} - IV_{j,t}^{i,\text{put}} \right) \right| \tag{1}$$

where $N_{i,t}$ is the total number of valid call-put pairs (same strike, same maturity) for stock $i$ on day $t$; $w_{j,t}^{i}$ is the open-interest weight; and $IV_{j,t}^{i,\text{call}}$, $IV_{j,t}^{i,\text{put}}$ are the implied volatilities. Only short-term options with time to maturity of 10 to 60 days are used. Daily $\text{Absoptivspread}_{i,t}$ is then averaged from July to the next May (11 months post-reconstitution) to form the annual dependent variable. A smaller value indicates better option market conditions (put-call parity more closely obeyed).

The alternative liquidity measure OptNZVD follows Liu (2006) and is the standardized turnover-adjusted number of zero trading volume days over $x$ months (equation (5), p. 12):

$$\text{OptNZVD}_{x} = \left( N_{0,x} + \frac{1/(x\text{-month turnover})}{\text{Deflator}} \right) \times \frac{21x}{\text{NoTD}} \tag{5}$$

where $N_{0,x}$ is the number of zero-volume trading days, $x\text{-month turnover}$ is the sum of daily options turnover (volume in shares divided by shares outstanding), NoTD is the number of trading days, and the Deflator ensures the fractional term lies in $(0,1)$. The paper uses $x = 11$ months (July through next May).

Empirical specifications

Main regression (option market conditions), equation (2), p. 5:

$$\text{Absoptivspread}_{i,t} = \tau \cdot \text{Dum2000}_{i,t} + \delta X_{i,t-1} + \text{FixedEffects} + \xi_{it} \tag{2}$$

where $\text{Dum2000}_{i,t}$ equals one when stock $i$ is at the top of the Russell 2000 in year $t$ (zero when at the bottom of the Russell 1000). $X_{i,t-1}$ is a vector of controls following Roll et al. (2010) and Lin and Lu (2015): log market capitalization in May (LNMAYSIZE), book-to-market ratio (B/M), cumulative daily stock return (LAGSTOCKRET), skewness of daily stock returns (LAGSTOCK_SKEW), log number of analysts (ANALYSTS), standard deviation of analyst earnings forecasts (DISPERSION), average stock bid-ask spread (STKSPREAD), average stock trading volume (STKVOL), mean open-interest-weighted implied volatility (IMPLIEDVOL), cumulative daily S&P 500 return (SP500), and average daily VIX (VIXYEAR). LNMAYSIZE is measured in May and B/M at the end of the previous fiscal year; the other controls are constructed over the same 11-month window as the dependent variable. Fixed effects include year and industry. The coefficient $\tau$ captures the indexing effect on option market conditions. The fully controlled specification uses 199 stock-year observations within the ±50-rank bandwidth, with year and industry fixed effects (Table 2, col. 3, p. 7). The table reports t-statistics in parentheses; the paper does not specify the standard-error estimator or clustering level.

Liquidity spillover regressions, equations (3) and (4), p. 7:

$$\text{Optvol}_{i,t} = \tau \cdot \text{Dum2000}_{i,t} + \delta X_{i,t-1} + \text{FixedEffects} + \xi_{it} \tag{3}$$ $$\text{Optspread}_{i,t} = \tau \cdot \text{Dum2000}_{i,t} + \delta X_{i,t-1} + \text{FixedEffects} + \xi_{it} \tag{4}$$

where $\text{Optvol}_{i,t}$ is the log of total options contracts and $\text{Optspread}_{i,t}$ is the open-interest-weighted daily average bid-ask spread in percent. Equations (3) and (4) use the same controls, year and industry fixed effects, 11-month July-to-May windows, and ±50-rank samples as equation (2). The fully controlled samples contain 368 stock-years for total options volume (Table 3, p. 8) and 368 for spreads (Table 4, p. 9). Tables 5 and 6 (pp. 10-11) estimate these outcomes separately for calls and puts: Table 5 has 316 observations per side; Table 6 has 363 put and 362 call observations. Each specification includes year and industry fixed effects. The paper reports t-statistics in parentheses and does not identify the standard-error estimator or clustering level.

Alternative-liquidity specifications, Tables 8-9, pp. 13-14:

$$\text{OptNZVD}_{i,t} = \tau \cdot \text{Dum2000}_{i,t} + \delta X_{i,t-1} + \text{FixedEffects} + \xi_{it}$$ $$\text{Optilliq}_{i,t} = \tau \cdot \text{Dum2000}_{i,t} + \delta X_{i,t-1} + \text{FixedEffects} + \xi_{it}$$

These use the same controls, year and industry fixed effects, 11-month July-to-May window, ±50-rank sample, and t-statistics in parentheses as the main regressions. Fully controlled samples are 321 stock-years for OptNZVD (Table 8, col. 3, p. 13) and 303 for Optilliq (Table 9, col. 3, p. 14). The article does not report the standard-error estimator or clustering level. OptNZVD is the standardized turnover-adjusted count of zero-volume days defined in equation (5). Optilliq is the average daily option price change divided by dollar volume, after adjustment for the option delta times the underlying stock price change. These measures adapt Liu (2006) and Amihud (2002), respectively, to options.

Robustness. Table 7 (p. 12) repeats the main regressions with bandwidths of ±25 and ±75 stocks. Fully controlled specifications retain negative and significant parity-deviation and spread coefficients and positive and significant volume coefficients at both bandwidths. Table 7 reports t-statistics in parentheses; it does not state a standard-error estimator or clustering procedure.

Datasets used

Dataset	Role in paper	Wiki page
OptionMetrics	Daily options data: strike price, trading volume, price, open interest, maturity, implied volatility, bid-ask spread, delta (for all exchange-traded options on sample stocks)	OptionMetrics (licensed)
CRSP	Daily stock price and trading volume for underlying stocks; used for control variables (STKVOL, LAGSTOCKRET, LAGSTOCK_SKEW)	WRDS / CRSP (licensed)
Compustat	Annual accounting data for control variables (book-to-market ratio B/M)	WRDS / Compustat (licensed)
Russell 1000/2000 Index membership lists	Annual index membership and ranking data (from Russell); used to identify Dum2000 and the threshold cutoff	No page yet

Sample: 1998-2006 (9 annual reconstitutions), 11-month estimation window per reconstitution (July through next May). Bandwidth: ±50 stocks around the Russell 1000/2000 cutoff. Final samples range from 199 (put-call parity regressions, Table 2) to 559 (options volume, Table 3) stock-year observations depending on options data coverage.

When to read the full paper

Use the original if you are: studying how equity market structure changes spill over into derivatives markets; extending the analysis to post-2007 reconstitutions or other index settings; distinguishing supply-side (market-making cost), demand-side (informed trading), and lending-fee channels in options markets; or building on the put-call parity deviation measure of Rösch et al. (2017) in an RDD setting. Tables 2-4 (pp. 7-9) contain the primary results; Tables 5-6 (pp. 10-11) contain the mechanism tests; Tables 7-9 (pp. 12-14) contain robustness.

Attribution and rights

Source: peer-reviewed, Journal of Financial Markets 78 (2026) 101026. This distillation was extracted by an LLM on 2026-06-25 and is not human-verified or independently reproduced. CC BY-NC-ND 4.0 license permits redistribution of verbatim copies; derivative works are not permitted. This page is an extract-only distillation; the PDF is not hosted.

Attribution (CC BY-NC-ND 4.0). Chang, Eric C., Li Ge, Tse-Chun Lin, and Xiaorong Ma. “The effect of stock market indexing on option market conditions.” Journal of Financial Markets 78 (2026): 101026. DOI: 10.1016/j.finmar.2025.101026. © 2025 The Authors. Published by Elsevier B.V. Licensed under CC BY-NC-ND 4.0. This page is an extract-only distillation by the Institute for Automated Research.