A Simple Random-Walk Markov Chain Simulation in Pine Script

Summary

This educational indicator generates one simulated price-like path using a simple Markov process and random draws. Starting from a user-defined value, each step selects an upward move, a downward move, or no move; the first two outcomes have equal stated chances, while staying in place is somewhat more likely. The magnitude of a nonzero move is randomly selected up to a configured deviation.

The script creates the path once on the first chart bar, then plots successive simulated values across bars up to the chosen iteration count. Its controls are the path length, starting value, and maximum deviation. This is an illustrative stochastic process, not a fitted market model: the document provides no calibration to historical prices, statistical diagnostics, repeated-simulation results, or evidence of predictive value. The label MCMC should therefore be read in light of the implementation shown, which demonstrates a random Markov chain rather than a complete inference workflow.

Key ideas

• The simulated path begins at a selected starting value and evolves one step at a time.
• Each step randomly moves up, down, or remains at the prior value.
• Nonzero move size is drawn randomly within the configured deviation.
• The path is generated once and plotted across chart bars until its iteration limit.
• The example is not calibrated to market data and gives no evidence of a trading edge.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.