Glossary term
Markov Chain
A Markov chain is a model for a sequence of states where the probability of the next state depends on the current state rather than the full path that came before.
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What Is a Markov Chain?
A Markov chain is a model for a sequence of states where the probability of the next state depends on the current state rather than the full path that came before. This idea is often called the Markov property.
Markov chains are used to model systems that move among defined states over time. In finance and economics, those states might be credit ratings, market regimes, default status, customer behavior, policy states, or portfolio conditions.
Key Takeaways
- A Markov chain models transitions from one state to another.
- The next-state probabilities depend on the current state.
- Transition probabilities are often organized in a matrix.
- Finance uses Markov chains in credit migration, regime models, risk analysis, and simulation.
- The model is useful, but it can oversimplify history-dependent behavior.
How a Markov Chain Works
A Markov chain starts with a set of possible states and probabilities for moving from each state to the next. For example, a bond issuer might remain investment grade, move to high yield, or default. A model can assign transition probabilities to those moves over a time period.
The transition probabilities can be placed in a transition matrix. Each row shows the current state. Each column shows the possible next state. The probabilities in a row usually add to 100%.
Simple Transition Matrix Example
Current state | Stay strong | Weaken | Default |
|---|---|---|---|
Strong | 85% | 14% | 1% |
Weak | 10% | 75% | 15% |
Default | 0% | 0% | 100% |
Financial Interpretation
Markov chains are useful when the state of a system matters more than the detailed path used to reach it. A credit model may care whether a borrower is currently rated BBB, not every rating change in the last decade. A market-regime model may care whether conditions are currently expansionary, recessionary, volatile, or calm.
The model can be used to estimate future distributions, expected time in a state, probability of default, or long-run behavior. It can also support simulation methods such as Markov Chain Monte Carlo.
Where the Model Can Mislead
The Markov property is a simplification. In real markets, history often matters. A company that just suffered a liquidity shock may not behave like every other company in the same current rating state. A market that has been volatile for months may not have the same transition probabilities as one that briefly spiked.
That does not make Markov chains useless. It means the model should be checked against data, stress scenarios, and the economic logic of the process being modeled.
The Bottom Line
A Markov chain models how a system moves from one state to another using current-state transition probabilities. It is useful in finance because many risk and forecasting problems can be framed as movement among states, but the simplifying assumptions need to be understood.