A Markov-chain market model represents market conditions as a small set of named states, typically something like calm, normal and stressed, with a transition matrix giving the probability of moving between them each period. Inside a token model it replaces a single volatility number with regimes that persist, so a bad month raises the odds that the next month is also bad. That persistence is what turns a survivable drawdown into an unlock, a reward promise and a treasury drawdown all landing inside the same stressed stretch.
The transition matrix, not the state definitions, is where the modelling risk sits. Estimating it needs enough history to have observed each regime several times, and a token with two years of price data does not have that, so the matrix gets borrowed from a longer-lived asset and silently imports its behaviour into your design.
States, transitions, and the memory a lognormal process does not have
The model has two parts. A set of states, each carrying its own parameters, so volatility, drift and often liquidity depth differ between calm and stressed. And a transition matrix, one row per state, giving the probability of being in each state next period given where you are now. The Markov property is the simplifying assumption: only the current state matters, not how you arrived in it.
The diagonal of that matrix is the whole reason to use one. If the probability of staying stressed given that you are stressed is high, the simulation produces runs of consecutive bad months rather than bad months scattered at random. Geometric Brownian motion with a fixed sigma cannot do this, because each of its steps is drawn independently. Clustering is exactly the property that decides whether a treasury survives, so the difference is not cosmetic.
The empirical case for regimes in crypto
This is not an aesthetic preference for realism. Caporale and Zekokh fit Markov-switching GARCH models to cryptocurrency returns, treating volatility as regime dependent rather than as one estimated number, and the work was published in the International Review of Economics and Finance.1 The regime structure is there in the data before anyone puts it in a token model.
Comparative work on the specification is ongoing. Markov-switching GARCH and stochastic volatility models have been compared directly, and the choice between them remains an open methodological question.2 Treat regime switching as a well-supported representation of crypto volatility, not the canonical one.
Where the transition matrix comes from, and why that is the weak point
Defining states is easy. Populating the matrix is not. Fitting transition probabilities requires enough history to have entered and left each state several times, and a token eighteen months old does not have it. What follows is predictable: the matrix gets estimated on Bitcoin or on a broad crypto index, then applied to a token whose liquidity, holder concentration and unlock calendar look nothing like Bitcoin's.
The substitution is defensible if you say you made it. Across the models we review it usually goes unstated, so the founder reading the output does not know that the persistence of stress in their own model is a property of a different asset. Record the estimation source next to the matrix, then rerun with the stress state made stickier and see how much of the result moves.
What regimes change in a token design
Four things move once conditions persist. Unlock timing, because the question stops being whether the market absorbs a cliff on average and becomes whether it absorbs one inside a sustained stressed run. Fee-funded buyback and burn mechanisms, because fee revenue and market stress are correlated, so the mechanism weakens exactly when it is needed. Treasury policy, because runway held in a volatile asset shortens in the same months revenue falls. And any reward promise denominated in fiat but paid in token.
The design consequence is usually the same one: mechanisms whose funding and their obligation move together are fragile, and a regime model is what makes that visible. A model with independent draws quietly averages the correlation away and shows you a mechanism that works fine.
State counts are a choice, not a finding
Two states or three, and where the boundaries sit, are decisions with no ground truth behind them. More states fit the history better and estimate worse, since each one divides an already thin sample. No procedure hands you the right number, so every regime model carries a specification choice its author should disclose.
Use it for what it is good at. It tells you whether your design depends on bad conditions being brief, which is a statement about your own mechanism and holds across a range of reasonable matrices. It is not a statement about what the market will do next, and this page does not make one.
Common questions
What is a Markov-chain market model used for in a token simulation?
It represents market conditions as a few named states with transition probabilities between them, so simulated conditions persist instead of resetting each period. In a token model that matters because stress clusters: unlocks, fee-funded buybacks and treasury runway all get tested against a sustained bad stretch rather than isolated bad months. It is the standard fix for the independence assumption in a lognormal price process.
How many market states should the model have?
Two or three is typical, and there is no correct answer. Each extra state fits the history more closely and is estimated from a smaller slice of data, so precision falls as realism rises. Since the choice is a judgement, state it with the results and check whether your conclusion survives a different specification. If it does not, the conclusion is a property of the state count rather than of your design.
How do you estimate the transition probabilities for a new token?
Usually you cannot, and that is the honest answer. Fitting a transition matrix needs repeated entries into and exits from each regime, which a token with a short price history has not produced. Teams borrow a matrix estimated on a longer-lived crypto asset, which is workable if disclosed. Run the model again with a stickier stress state to see how much of the result rests on that borrowed number.
See Tokenomics Design for how this applies in practice.
Sources
- Modelling Volatility of Cryptocurrencies Using Markov-Switching GARCH Models
Guglielmo Maria Caporale and Timur Zekokh, Brunel University London, Economics and Finance Working Paper No. 18-10; published in International Review of Economics and Finance vol. 48, 2018
Fits regime-switching volatility models to cryptocurrency returns. Journal record at ideas.repec.org/a/eee/riibaf/v48y2019icp143-155.html. - Comparison of Markov Switching GARCH and Stochastic Volatility Models
arXiv:2401.03393, 2024
Methodological comparison of the two specifications, cited here for the point that the choice between them is an open question rather than a settled one.
Last reviewed 2026-08
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