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Using Student-t Increments to Simulate Asset Paths

Article Quant Q&A · Author: lechim
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Summary

The document raises a modeling question about changing a geometric Brownian motion simulation so that its increments are generated from a Student-t distribution rather than a normal distribution. This substitution produces heavier-tailed increments and is presented as an experiment by someone seeking to simulate an asset path.

The source contains no response, derivation, or empirical comparison, so it does not establish whether this construction is appropriate. A Student-t increment sequence alone does not ensure the desired asset dynamics: distribution scaling, degrees of freedom, finite moments, drift, and the relationship between simple or log returns and price levels all matter. The question is useful as a prompt to distinguish a change in return distribution from a complete asset model, but offers no evidence or guidance for calibration or validation.

Key ideas

  • Replacing normal draws with Student-t draws changes the tails of simulated increments.
  • The document applies this substitution within a geometric Brownian motion path simulation.
  • A return distribution choice does not by itself specify a complete asset price model.
  • The source asks whether the approach is valid but supplies no answer or evidence.

Tags

StatisticsRisk managementBacktesting
Full text
# student-t asset path


# student-t asset path












I am trying to simulate an asset path based on a t-distribution. I found a lot of ressources and the fact that it will be difficult to do a path. But now I changed my Geometric Brownian Motion Simulation and instead of using normal random numbers, I take random student-t numbers using the Matlab-command trnd. So I get a new path and the increments are student-t distributed. Now I don't know if this is a totally wrong approach, since I am more or less a beginner in quantitative finance.

Thank you for your help Kind regards

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