Constrained Random Walks for Simulating Intrabar Market Price Paths
Summary
This article develops a supervised random-walk approach for generating plausible price paths inside recorded market bars for a replay simulator. A simple free random walk can look stochastic, but it may fail to visit a bar’s specified high, low, or close. The simulator must honor those recorded values while producing more varied paths than a fixed zigzag model.
The method constrains movement to the bar’s price range and divides the path into segments that ensure the required points are reached. The article describes shaping the final segment with alternating additions and subtractions, which can produce a symmetric or asymmetric triangular pattern depending on the relative locations of the starting, extreme, and ending prices. The illustrations compare a zigzag, unrestricted random values, an ordinary random walk, and the constrained result.
This is a path-generation design for replay and simulation, not a model validated against tick-by-tick market behavior. Its examples are schematic, and meeting OHLC constraints does not establish that the generated sequence reproduces actual order flow or execution conditions.
Key ideas
- A free random walk may fail to touch every price point required by a recorded bar.
- The proposed path stays within the bar’s range and is structured to reach its open, high, low, and close.
- Segmented movement and alternating steps shape the path while allowing different triangular forms.
- The article uses schematic graphs to compare path-generation approaches, not empirical market validation.
- OHLC-consistent simulated paths do not by themselves capture intrabar trading or execution dynamics.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.