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Using Lévy Processes to Model Sudden Price Drops

Article Quant Q&A · Author: LuaLua
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Summary

The document asks what price process can represent a perceived pattern in which prices rise gradually but fall abruptly. It contrasts this intuition with geometric Brownian motion, whose continuous paths do not contain sudden jumps, and points to Lévy processes as a broader class of models that can include jumps.

The response offers a direction for further study rather than a complete model specification. It does not select a particular Lévy process, explain how to estimate its parameters, or provide empirical evidence that price declines systematically differ from gains. A practical model choice would need to reflect the asset, sampling interval, and intended use, and should be assessed against observed return distributions and jump behavior.

Key ideas

  • Geometric Brownian motion models continuous price paths and cannot produce instantaneous jumps.
  • Lévy processes extend Brownian motion with processes that can include jumps.
  • The document does not identify a specific jump model or provide calibration guidance.
  • The suggested asymmetry between gradual rises and abrupt declines is posed as an intuition, not demonstrated evidence.

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StatisticsVolatility
Full text
# Geometric brownian motion and sudden price drops


# Geometric brownian motion and sudden price drops












Simple question of a curious person:

One can say that prices tend to rise "slowly" and drop "all of a sudden". Still, they are a geometric composition upon random returns.

As I understand, this is not a feature of a geometric brownian motion.

If so, what would be a standard price process consistent with this behavior?

Best!

## Answer by Ezy (score 0, accepted)

https://quant.stackexchange.com/a/42286

The natural extension of Brownian motion that includes jump are called Levy processes

https://en.wikipedia.org/wiki/L%C3%A9vy_process

probably you want to look into those.

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