# Kyle Model: Insider Trading and Price Impact

Trade as the insider in the Kyle model: hide orders in noise trading, watch the price impact λ × order flow and see prices learn the secret.

## About this tool

In the Kyle model one insider knows the true value of an asset, noise traders submit random orders, and a market maker sees only the total order flow. The maker cannot tell the insider's orders from the noise, so it sets the price as a linear function of the flow: Δp = λ × order flow, where λ, Kyle's lambda, measures price impact. The insider wants to profit from the information but knows that trading aggressively moves the price against them. The optimal strategy trades gradually and hides in the noise, so that the information leaks into the price at a steady pace. This lab puts you in the insider's seat.

## Frequently asked questions

### What is Kyle's lambda?

It is the price impact per unit of order flow: if the net order flow is x, the price moves by λx. A large λ means a thin, illiquid market where every order moves the price a lot; a small λ means a deep market. In the model λ grows with the uncertainty about the value and falls with the amount of noise trading, because more noise gives the market maker less reason to read flow as information.

### Why does the insider not trade everything at once?

Because a large order would be read as information and move the price to the true value immediately, leaving almost no profit. By spreading trades out, the insider keeps each round's order small relative to the noise, so the price adjusts only partly each time. In the continuous version the insider trades so that the price converges to the true value exactly at the end.

### Who loses money to the insider?

The noise traders. The market maker sets prices so that it breaks even on average, so the insider's expected profit comes entirely from the noise traders, who buy and sell for reasons unrelated to the value. More noise trading means more camouflage and a larger profit for the insider, but also a smaller loss per noise trade.

### What should I try in the lab?

Play a few rounds as the insider and compare your profit with the optimal strategy on the same seed. Then try trading all at once and see the price jump to the value. Finally estimate λ by drawing a line through the scatter of order flow against price change. A common misconception is that price impact is a cost of trading large orders only; here it is how information gets into prices.

## Learn the theory

- [Informed trading and Kyle's lambda](https://quantsandbox.dev/guide/microstructure/kyle-model): An insider hiding among noise traders, a market maker who prices from total order flow, the price-impact coefficient λ, and why the insider trades gradually.
- [Price impact and optimal execution](https://quantsandbox.dev/guide/microstructure/price-impact): Temporary and permanent impact, the square-root rule of thumb, splitting a large order over time, and the Almgren–Chriss trade-off between cost and risk.

Open the interactive tool: https://quantsandbox.dev/kyle