A smarter model of insider trading — and what it tells us about how markets really work
Markets are not neutral. Every trade is a signal, and sophisticated participants know it. The question is: how does an informed trader extract value from private information without giving the game away? And how does a market maker set prices when they can only observe the combined flow of informed and uninformed demand? This is the core of the Kyle model — first introduced in 1985 and still one of the most influential frameworks in market microstructure research. A new paper by Dr. Christoph Kühn and Dr. Christopher Lorenz, published in Mathematics and Financial Economics (2025), significantly extends this framework for real-world markets where asset values and order flows don’t follow the convenient Gaussian distributions that classical models assume.
Three players, one information edge. The model captures a situation familiar to any practitioner: a trader who knows something the market doesn’t, a stream of uninformed order flow providing camouflage, and a market maker who must quote prices based only on what they can observe. The insider trades strategically across multiple rounds — not dumping the full position at once, but parcelling out orders to avoid moving prices too quickly and revealing the information advantage. The market maker, knowing an insider may be present, adjusts prices upward on net buying and downward on net selling. It’s a cat-and-mouse game, and the paper asks: does a stable outcome even exist?
The classical model’s hidden assumption. Kyle’s original result depends on a key shortcut: all uncertainty is normally distributed. Under that assumption, the insider’s optimal strategy is a clean linear rule — buy or sell a fixed proportion of the information gap each period — and the market maker can price efficiently in response. The math is elegant, but the assumption is fragile. Real asset values are skewed, fat-tailed, and sometimes discrete (think credit ratings, earnings surprises, or regulatory outcomes). Real order flow is lumpy and non-Gaussian. The moment you drop normality, the linear equilibrium breaks down entirely.
Why insiders must randomise. The key insight of the paper is that, without Gaussian distributions, an informed trader cannot follow a mechanical rule. If the insider always buys exactly the same quantity for a given signal, a sharp market maker will eventually decode the pattern and price out the information edge. The only sustainable strategy is deliberate unpredictability: the insider must randomise — not because of risk aversion, but as a rational competitive response to being watched. This is not just a theoretical quirk. It mirrors observed behaviour: sophisticated block traders vary order sizes, use algorithmic randomisation, and split execution across venues precisely to prevent information leakage. The paper gives this practice a rigorous equilibrium foundation.
Prices can move in unexpected directions. One of the more striking results is that the market maker’s pricing response need not be monotone in total order flow. In the Gaussian world, more buying always pushes prices up. Under general distributions, there are configurations where a large buy order actually triggers a price decrease — because the market maker infers that such an extreme order is more likely noise than information. This has direct implications for execution: large institutional orders can, under certain market conditions, move prices in counterintuitive directions, and strategies calibrated on Gaussian models may perform poorly or generate unexpected market impact.
What this means for market structure and regulation. The framework speaks directly to live policy debates. Payment for order flow — where brokers sell retail order flow to market makers — is under scrutiny in both the US and Europe precisely because it affects the mix of informed and uninformed flow reaching any given venue. This model clarifies the mechanics: the value a market maker extracts depends critically on how much noise flow insulates them from adverse selection. Change that mix — through regulatory reform, venue fragmentation, or dark pool growth — and the equilibrium pricing and information transmission properties of the market shift in ways that linear Gaussian models cannot capture. The takeaway for practitioners and regulators alike is that market microstructure is more sensitive to distributional shape than standard models suggest, and that robust analysis requires frameworks that do not assume problems away.