Regulating Over-the-Counter Markets: Lee & Wang (2025)

What this is. This is the distilled skeleton of Lee and Wang (2025), “Regulating Over-the-Counter Markets,” J. Finance 80(4): 1929-1962. It extracts the model, propositions, and key theoretical results with PDF locators. Read the original paper to replicate or extend.

TL;DR

Lee and Wang (2025) embed dealer cream skimming via price discrimination into the standard Glosten and Milgrom (1985) exchange model, allowing the OTC dealer to observe a public label (Likely Informed vs. Likely Uninformed) before quoting. The venue-choice between OTC and exchange follows Seppi (1990); the label-dependent pricing and cream skimming also relate to Desgranges and Foucault (2005), who show how dealer-client relationships concentrate adverse selection on exchanges. In equilibrium LI traders go to the exchange and LU traders go to the OTC market. The paper’s central finding is that restricting the dealer’s ability to discriminate across labels always reduces aggregate volume and widens the average spread, yet can raise utilitarian welfare whenever adverse selection risk (the mass of informed traders) is low. The mechanism is “cheap substitution”: pooling causes uninformed traders with larger hedging benefits (previously on the exchange) to enter while uninformed traders with smaller benefits (previously in the OTC market) exit, and the entrants more than offset the exiters in welfare terms when adverse selection risk is low. This contradicts Bolton, Santos, and Scheinkman (2016), who find cream skimming raises welfare via origination effort incentives. The model also contrasts with Akerlof (1970): the paper shows cheap substitution reverses in that standard framework because private and common values are perfectly correlated there. On the price discrimination side, Bergemann, Brooks, and Morris (2015) show that without adverse selection any welfare outcome is achievable; this paper shows adverse selection provides robust guidance. The paper derives an optimal Pigouvian tax on OTC trades and a simple implementable “WSR Rule” based on the ratio of exchange to OTC spreads and volume changes, without requiring knowledge of structural parameters.

Core results

#	Result	Locator	Magnitude as reported
R1	Welfare effect of restricting OTC dealer: raises welfare when informed mass μ is small, lowers it when μ is large	Proposition 2, pp. 1938-1939	Single cutoff under quasiconcave ΔW; any commonly used F satisfies conditions
R2	Volume and spread always worsen under restriction	Proposition 2(e), p. 1939	Aggregate volume V strictly falls and average spread S̄ strictly widens for all μ > 0, under any distribution with decreasing ΔV
R3	Optimal Pigouvian tax dominates OTC closure	Proposition 5, p. 1944	T* strictly raises welfare above closing the OTC market for any (α, θ, γ); unique under U[0,1]
R4	WSR Rule implements T* without structural estimation	Proposition 6, pp. 1944-1945	WSR(T) > 1: raise T; WSR(T) < 1: cut T; WSR = 1 at T*; WSR ≡ |S_E dV_E / (S_O dV_O)|
R5	High OTC market share is not evidence against restriction	Proposition 4, pp. 1942-1943	OTC share V_O/V is decreasing in μ; restriction raises welfare exactly where OTC share is high
R6	Empirical: exchange spread and exchange share positively correlated across U.S. equities	Internet Appendix §VI.C	Positive correlation of quoted spread with exchange market share corroborates model prediction

Overall (paper’s conclusion). Trading costs, volumes, and market shares can all mislead regulators because cheap substitution decouples these aggregates from welfare. The adverse selection parameter β, not aggregate volume or OTC share, is the correct policy signal. When β is low, restricting OTC price discrimination strictly improves welfare and the optimal tax can be approximated by the WSR statistic computed from observable trade data.

Theory / model

The paper has no empirical design; the identification is structural (model restrictions). The model and propositions are the core content.

Setup. A continuum of risk-neutral traders may trade an indivisible asset in a three-stage game (Figure 2, p. 1935). The asset pays $v \in \{-1, +1\}$ with equal probability. A mass μ of traders are informed (private binary signal $s_i = v$ with probability α and $-v$ otherwise; α is signal accuracy). A mass 1 of uninformed traders each draw a hedging benefit $b_i \overset{\text{iid}}{\sim} F$ with support $[0,1]$. Each trader is publicly labeled $\ell_i \in \{\text{LI}, \text{LU}\}$; the odds of being informed conditional on label LI exceed the unconditional odds:

$\mathcal{O}_{LI} = \frac{\theta\mu}{1-\gamma} > \mu > \frac{(1-\theta)\mu}{\gamma} = \mathcal{O}_{LU}$

where $\theta < 1$ is the probability an informed trader is labeled LI and $\gamma < 1$ is the probability an uninformed trader is labeled LU.

Equilibrium. Each trader chooses to buy, sell, or exit on the exchange, over the counter, or not trade (Definition 1, p. 1936). The OTC dealer observes the label $\ell_i$ before quoting; the exchange dealer does not and sets a single unconditional spread. The zero-profit condition for the dealer posting spread $s$ when the informed ratio in her pool is $\beta$ is (p. 1937, Eq. 2):

\underbrace{s \cdot (1 - F(s))}_{\text{Profit from uninformed}} = \underbrace{(2\alpha - 1 - s)^+ \cdot \beta}_{\text{Loss to informed traders}} \tag{2}

The unique solution $S(\beta)$ is increasing in $\beta$.

Proposition 1 (equilibrium spreads, p. 1937). The exchange spread is $S_E = S\!\left(\frac{\theta}{1-\gamma}\mu\right)$; the OTC spread for LU traders is $S_O = S\!\left(\frac{1-\theta}{\gamma}\mu\right)$ and for LI traders is $S_E$. LI traders choose the exchange, LU traders choose the OTC market. The exchange spread strictly exceeds the OTC spread: $S_E > S_N > S_O$ where $S_N = S(\mu)$ is the no-OTC spread.

Welfare and volume. Welfare $W$ equals the sum of hedging benefits of uninformed traders who trade. The average bid-ask spread is $\bar{S} \propto 1/V$. Two quantities characterize the restriction’s effect (pp. 1937-1938):

\Delta_V(\beta) := -\!\left(\int_{S(\beta)}^1 f(s)\,ds\right)' = S'(\beta)\cdot f(S(\beta)) \tag{3}

\Delta_W(\beta) := -\!\left(\int_{S(\beta)}^1 sf(s)\,ds\right)' = \Delta_V(\beta)\cdot S(\beta) \tag{4}

Marginal volume $\Delta_V$ is the fall in uninformed trade per unit increase in $\beta$; marginal welfare $\Delta_W$ equals $\Delta_V$ times the marginal exiter’s hedging benefit $\bar{b}(\text{exiters}) = S(\beta)$.

Proposition 2 (main result, pp. 1938-1939). For any commonly used distribution F, restricting the OTC dealer:

• (a)-(c): raises welfare W if $\mu < \mu_l$ (small informed mass) and lowers W if $\mu > \mu_h$;
• (d): if $\Delta_W$ is strictly quasiconcave, the two cutoffs collapse to one: restriction raises W iff $\mu < \underline{\mu}$;
• (e): always strictly reduces aggregate volume V and strictly widens average spread $\bar{S}$.

Proposition 3 (sufficient conditions, p. 1941). $\Delta_W$ is strictly quasiconcave iff

\frac{(2\alpha-1)(1-F(x))}{xf(x)(2\alpha-1-x)^2} - \frac{1}{2\alpha-1-x} \quad\text{is strictly quasiconvex on }(0,2\alpha-1). \tag{5}

Any Beta(a, b) distribution satisfies (5) for all $a,b > 0$.

Proposition 4 (market shares, pp. 1942-1943). Under condition (7) (satisfied by uniform and beta distributions), OTC share $V_O/V$ is strictly decreasing in $\mu$. Therefore restricting the OTC dealer raises welfare precisely where the OTC market share is high, directly overturning the industry argument that high OTC share signals OTC efficiency.

Method

This is a pure theory paper with no structural estimation. The solution method is closed-form zero-profit conditions plus comparative statics via the Implicit Function Theorem and integral inequalities. Proofs are in the Appendix (pp. 1949-1962).

Pigouvian tax characterization. A lump-sum tax $T$ on OTC trades shifts the dealer zero-profit conditions to (pp. 1943-1944):

S_O(T)\cdot\left[1-F(S_O(T))+\beta_O\right]\gamma = (2\alpha-1)\beta_O\gamma + T \tag{8}

S_E(T)\cdot\left[1-F(S_E(T))+\beta_E\right](1-\gamma) = (2\alpha-1)\beta_E\cdot(1-\gamma) - T \tag{9}

All implementations that raise the same gross revenue T are equivalent. The optimal Pigouvian tax T* maximizes welfare W. Proposition 5 (p. 1944) shows T* strictly dominates OTC market closure.

WSR Rule (Proposition 6, p. 1945). Define the Weighted Spread Ratio:

\text{WSR}(T) := \left|\frac{S_E(T)\,dV_E(T)}{S_O(T)\,dV_O(T)}\right| \tag{10}

The welfare-increasing direction of T is: raise T when WSR > 1 (cheap substitution dominates), cut T when WSR < 1 (volume effect dominates). The optimal tax satisfies WSR(T*) = 1. The ratio $S_E/S_O$ is observable as the ratio of exchange to OTC spreads; $|dV_O/dV_E|$ is the ratio of volume changes before and after a policy perturbation.

Empirical specifications

The paper is theoretical; there is no estimation. The Internet Appendix (Sections V and VI) documents supporting empirical patterns without a causal design.

Empirical pattern 1 (Internet Appendix §V). The exchange’s market share and spread are positively correlated because both are driven by the informed ratio β. As β rises, the OTC market absorbs more informed traders so the exchange spread rises and OTC share rises mechanically.

Empirical pattern 2 (Internet Appendix §VI.C). The total market share of exchanges and their quoted spreads are positively correlated across U.S.-listed equities, corroborating the model prediction (p. 1933). This is documented as a novel empirical pattern, not a causal test.

The paper explicitly leaves causal estimation of the welfare effects of OTC restrictions for future work.

Datasets used

Dataset	Role in paper	Wiki page
U.S. equity market microstructure data (quoted spreads, exchange market share)	Empirical corroboration in Internet Appendix §VI.C	no page yet

The core model is theoretical; no large dataset is used for estimation.

When to read the full paper

Read Lee and Wang (2025) when:

• Designing or evaluating OTC market regulations (post-trade transparency, name give-up rules, blockchain record-keeping proposals discussed in the Internet Appendix §I);
• Studying how to implement a Pigouvian tax on OTC trading without needing structural estimates of adverse selection risk, using the WSR Rule;
• Understanding why aggregate volume, average spread, and OTC market share are unreliable welfare indicators in two-venue markets;
• Modeling OTC-versus-exchange venue choice with imperfect trader labels in a Glosten-Milgrom framework.

The key propositions (Propositions 2, 4, 5, 6) are in §II and §III (pp. 1938-1945). Appendix proofs are pp. 1949-1962.

Attribution and rights

This article is open access under CC BY 4.0. The canonical citation is:

Lee, Tomy and Chaojun Wang. “Regulating Over-the-Counter Markets.” The Journal of Finance 80, no. 4 (August 2025): 1929-1962. https://doi.org/10.1111/jofi.13461

Copyright 2025 The Authors. Published by Wiley Periodicals LLC on behalf of American Finance Association. Open access funding provided by Central European University Private University - CEU GmbH/KEMO.

This page is LLM-distilled by the IAR paper-distiller (claude-sonnet-4-6). It is not human-verified and the results have not been independently reproduced. Extract-only; the original PDF is not mirrored here (CC BY 4.0 permits redistribution by any party with proper attribution).