Geometric Brownian motion is the standard stochastic process for modeling asset prices in a simulation, defined by a drift rate and a volatility coefficient. Each Monte Carlo path draws a randomized price trajectory from it, capturing both an expected trend and realistic price noise.
GBM is not a price forecast. Its job is to generate a plausible range of price environments the design must survive, especially the low-percentile paths.
How it works
GBM is a continuous-time process in which the logarithm of price follows a random walk with constant drift and constant volatility. In discrete form, next period's price equals this period's price times the exponential of the drift term plus a normally distributed shock scaled by volatility. Two parameters define it: mu, the expected rate of change per period, and sigma, the standard deviation of that change.
For tokenomics simulation, each of the thousand Monte Carlo paths generates a unique multi-year price trajectory by drawing a fresh sequence of random shocks. The collection produces a fan of outcomes, and the width of that fan is set almost entirely by the volatility parameter.
Where its limits matter
GBM assumes log-returns are normally distributed, but token prices show fat tails and volatility clustering: large moves happen more often than the normal distribution predicts, and volatile periods persist. It also assumes constant volatility, while real token volatility runs higher during downturns. This is why the Markov-chain market model extends GBM, shifting volatility and drift as market state changes to capture some of that clustering.
The practical implication: set volatility from a stressed sample, not a recent calm-market window. If comparable projects ran 120% realized volatility during adverse markets, using 60% because the last few months were quiet will systematically understate the spread in the tail paths.
Common mistake
Treating GBM output as a price prediction. GBM is a null hypothesis about how prices move, not a model with predictive power for a specific token. The question is never what price GBM predicts. The question is whether the design survives the low-percentile price paths it generates.
See Tokenomics Design Services for how this applies in practice.
Know the terms but not sure how they apply to your project? That is what an engagement is for. We design, document, and stress-test the whole token economy inside the Tokenomics Data Room.
80+ projects advised. Complete tokenomics in 4 to 6 weeks.