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Strategic OTC market making with reputation feedback

This paper introduces a stochastic-control model for electronic OTC market making that incorporates reputation feedback mechanisms, demonstrating how dealers must strategically balance immediate spread capture against long-term franchise value to navigate alternating phases of reputation building and monetization.

Original authors: Alexander Barzykin

Published 2026-07-14

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Alexander Barzykin

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are a lemonade stand owner in a very busy, high-tech town. In the old days, your only job was to decide how much to charge for a cup of lemonade right now. If you charged a little more, you made more profit per cup, but maybe fewer people bought it. If you charged less, you sold more, but made less profit. It was a simple math problem: Price vs. Sales.

But this paper suggests that in today's electronic markets, it's not just about the price of the next cup. It's about your reputation score with the town's mayor and the neighborhood kids.

The Two Games You're Playing

The paper sets up a scenario where a dealer (that's you, the lemonade seller) is playing two different games at the same time, and your performance in one affects the other.

The "Request" Game (Tier A): Imagine a kid runs up and asks, "How much for a lemonade?" You shout a price. If your price is good, they buy (you "win" the request). If it's too high, they walk away. Your score here is your Win Ratio.
The "Streaming" Game (Tier B): Imagine a continuous stream of kids running by, and you have to shout prices to them instantly. Sometimes, a kid runs up, you shout a price, but the wind (or a delay) makes your voice sound different to them. If the deal looks bad for you because of the wind, you can say, "Actually, never mind," and reject the trade. Your score here is your Fill Ratio (how many times you actually let a trade happen versus how many you rejected).

The Secret Sauce: The "Gatekeeper"

Here is the twist the paper introduces: The town has a magical gatekeeper.

If your Win Ratio is high, the gatekeeper invites more kids to ask you for prices.
If your Fill Ratio is high, the gatekeeper sends more kids running by your stand.
But if your scores drop? The gatekeeper stops sending kids. You might get ignored, or only get sent the "toxic" kids (the ones who are trying to trick you).

So, you aren't just trying to make money on the current cup. You are trying to manage your reputation score to keep the gatekeeper happy.

The Big Trade-Off: "Campaigning" vs. "Cashing In"

The paper's main finding is that the smartest strategy isn't just "always make the most money." It's a cycle of two very different moods:

The "Reputation Campaign" (The Aggressive Phase):
Imagine your score is low. The gatekeeper is barely sending anyone. To fix this, you might decide to sell lemonade for almost nothing (or even a tiny loss). You are "buying" wins. You are sacrificing immediate profit to boost your Win Ratio or Fill Ratio. The paper calls this a "reputation-building campaign." You are playing the long game to get invited back to the party.
The "Franchise Monetization" (The Cautious Phase):
Once your score is high and the gatekeeper is flooding you with customers, you can relax. You can raise your prices. You can be pickier about which trades you accept. You are now "monetizing" your strong reputation. You make more profit per cup because you have a steady stream of customers.

The paper suggests that if you try to be greedy all the time, you might lose your score, get cut off by the gatekeeper, and end up with no customers at all. But if you know when to be cheap and when to be expensive, you can stay in business.

The "Bistability" Surprise

Here is the most fascinating part, found in the paper's computer simulations: Two dealers can be exactly the same, but end up in totally different worlds.

Imagine two lemonade stands with the exact same lemons, the same sugar, and the same risk tolerance.

Dealer A started with a slightly better reputation. They got more customers, built a better score, and now they are the "King of the Hill," making huge profits.
Dealer B started with a slightly worse reputation. They got fewer customers, their score dropped, they got rejected more often, and they are stuck in a "marginal" state, barely surviving.

The paper shows that the system has two stable states: a "High-Reputation Leadership" state and a "Low-Reputation Marginal" state. Once you fall into the low state, it's very hard to climb out, even if you change your strategy. The path you take matters just as much as the strategy you use.

What the Paper Doesn't Say

It's important to know what this paper is not claiming.

It does not say that "Last Look" (the ability to reject a trade) is always good or always bad. It says it's a tool. If you use it too much, your Fill Ratio drops, and the gatekeeper punishes you. If you use it too little, you lose money on bad trades.
It does not claim that this is a solved problem for every bank. The results come from a mathematical model and computer simulations (using specific numbers like a daily volatility of 100 bp and a risk aversion of 5 · 10⁻⁴ bp⁻¹ M⁻¹). It suggests how things might work, not how they definitely work in every single real-world scenario.
It does not say that you should ignore the price of the lemonade. The price still matters; it's just that the price now has a second job: managing your reputation.

The Takeaway

In the past, market makers were like robots just trying to catch the best price. This paper suggests they are more like social climbers.

Every time you quote a price, you are making two moves:

You are trying to make a profit on the trade.
You are casting a vote for your future reputation.

Sometimes, the smartest move is to take a small loss on the trade today so you can win the game tomorrow. The paper uses complex math (like Hamilton-Jacobi-Bellman equations and adiabatic approximations) to prove that this "reputation feedback" creates a system where dealers naturally switch between being aggressive campaigners and conservative cashiers, and where a small difference in starting luck can lead to a huge difference in final success.

So, the next time you see a lemonade stand owner selling a cup for a penny, don't just think they are desperate. They might just be running a "reputation campaign" to make sure the gatekeeper keeps the floodgates open for tomorrow.

Technical Summary: Strategic OTC Market Making with Reputation Feedback

Problem Statement

In electronic Over-the-Counter (OTC) markets, liquidity provision has evolved from a sequence of independent quote optimizations into a dynamic franchise problem. Dealers face a critical trade-off: optimizing immediate spread capture versus maintaining or improving their "standing" with clients and platforms. This standing is quantified by performance metrics such as Request-for-Quote (RFQ) win ratios and streaming fill ratios, which directly influence future flow allocation through performance-based gates.

Classical stochastic market making models typically treat request intensities and fill probabilities as exogenous. However, in practice, access to future flow is an endogenous state variable influenced by a dealer's current quoting and acceptance decisions. A dealer who loses too many RFQs or rejects too many streaming requests may be down-weighted or excluded from future opportunities, while strong performance can secure leadership positions, albeit with increased inventory and toxicity exposure. The paper addresses the need for a tractable control framework that explicitly models this feedback loop between execution quality and future opportunity sets.

Methodology

The authors develop a stochastic optimal control model featuring two distinct execution protocols:

Tier A (RFQ): Characterized by a win-ratio score ( $R_A$ ). The dealer controls quote offsets ( $\delta$ ) to maximize the probability of winning a request, which updates the score based on success or failure.
Tier B (Streaming): Characterized by a fill-ratio score ( $R_B$ ). The dealer controls both quote offsets ( $\delta$ ) and a non-negative rejection threshold ( $\eta$ ) for a "fair" last-look protocol. This protocol manages adverse selection (modeled via a Gaussian latency mark) by rejecting trades with excessive negative slippage while capping positive slippage.

Mathematical Framework

State Variables: The system includes fast variables (inventory $Q_t$ , cash $X_t$ , mid-price $S_t$ ) and slow variables (reputation scores $R_A, R_B$ ).
Objective: Maximize expected terminal mark-to-market wealth penalized by inventory risk and running costs, subject to the dynamics of the reputation scores.
Hamilton-Jacobi-Bellman (HJB) Equation: The problem is formulated as an HJB equation with two slow reputation variables and a fast inventory state.
Adiabatic Approximation: To make the problem tractable, the authors employ a slow-fast (adiabatic) approximation. They assume the reputation scores change slowly ( $\alpha_\tau \ll 1$ $α_{τ} ≪ 1$ ) relative to inventory dynamics.
- Fast Problem: For a "frozen" reputation state, the dealer solves the standard inventory control problem.
- Slow Dynamics: The induced policy from the fast problem is averaged over the stationary inventory distribution to derive deterministic drift equations for the reputation scores.
Reduction: This approach reduces the high-dimensional stochastic control problem to a two-dimensional deterministic system for the reputation scores, preserving the economic feedback loop while clarifying the strategic dynamics.

Key Contributions

Endogenous Flow Modeling: The paper provides a compact framework where future flow intensity is a function of current execution quality, mediated by score-dependent gate functions.
Unified Control of Quotes and Rejections: The model jointly optimizes quote offsets and, for streaming, a last-look threshold, treating the rejection mechanism as an option-like barrier to manage toxicity while maintaining fill ratios.
Strategic Phase Separation: The derived optimal policy naturally alternates between distinct phases:
- Reputation Building: Sacrificing immediate spread (tightening quotes) to win RFQs or fill streaming requests to improve scores.
- Franchise Monetization: Widening spreads to capture value once a strong reputation is established.
- Defense: Maintaining conservative settings to prevent falling below critical thresholds.
Bistability and Path Dependence: The model demonstrates that performance-based gates can lead to multiple stable equilibria (bistability). A dealer's long-term regime (marginal vs. leading) depends on initial conditions and the sequence of recovery, not just current parameters.

Numerical Results

Using a policy iteration scheme on a discretized grid, the authors simulate the model with calibrated parameters for RFQ and streaming tiers.

Promotion Values: The marginal value of a successful event (winning an RFQ or filling a stream) is highly state-dependent, peaking near the "gate" thresholds where a single success can trigger a regime shift, rather than when the dealer is already a leader.
RFQ Dynamics: Near the gate midpoint, the dealer aggressively narrows spreads to improve win probability. Above the gate, spreads widen to monetize flow, though the policy remains defensive to avoid falling back.
Streaming Dynamics: When the fill ratio is low, the dealer tightens spreads to the floor to generate more requests and repair the score, while retaining a rejection threshold to filter toxic flow. As the score improves, the dealer widens spreads and becomes more tolerant of flow.
Phase Portrait: The two-dimensional reputation dynamics exhibit two attracting equilibria: a low-reputation "marginal" state and a high-reputation "leadership" state. The system displays path dependence; the order in which scores recover (e.g., repairing streaming first vs. RFQ first) determines the trajectory through the state space. Cross-tier spillovers occur via shared inventory and continuation value, though they are modest under baseline calibration.

Significance and Claims

The paper claims to make the intuition of "dynamic relationship management" in OTC markets explicit within a tractable stochastic-control setting. It argues that optimal behavior is not merely myopic spread optimization but a strategic allocation of competitiveness across different time horizons.

Key conceptual conclusions include:

State-Dependent Marginal Value: The value of a win or fill is highest when the dealer is near a promotional threshold, not necessarily when they are already dominant.
Contextual Aggressiveness: A quote's aggressiveness is determined by its strategic purpose (building reputation, defending access, or monetizing) rather than static risk parameters.
Multiple Regimes: Reputation feedback can create self-reinforcing cycles where a dealer with identical technology and risk appetite may remain trapped in a low-flow state or ascend to a leadership position depending on initial conditions and the steepness of client-routing gates.

The authors suggest these findings provide a modeling language for practical e-trading decisions, such as when to invest in competitiveness, when to tolerate toxic flow, and how to manage portfolio-level score dynamics rather than isolated quote decisions.