How do transition probabilities generate volatility persistence in a two-state market model?

Conditions

• The market is modeled as a two-state Markov chain.
• Self-transition probabilities are high relative to switching probabilities.

Reasoning, step by step

1. Identify the two states: Low and High volatility.
2. Read the self-loop probabilities: 0.8 for Low, 0.7 for High.
3. Read the cross-transition probabilities: 0.2 for Low to High, 0.3 for High to Low.
4. Interpret the large self-loops as the tendency for the current regime to persist.
5. Conclude that persistence emerges directly from the transition structure.

Example

The diagram shows P(Low→Low)=0.8 and P(High→High)=0.7. The narrator explains that low volatility usually remains low and high volatility tends to persist.

Common misconceptions

• Believing that persistence must be added by hand as an extra rule.
• Assuming that switching probabilities are higher than staying probabilities in this example.

Watch the explanation

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