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Why the Heston Feller Condition Matters Beyond Simulation

Article Quant Q&A · Author: Xerium
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Summary

The document asks why researchers impose the Feller condition when solving the Heston stochastic volatility model with finite difference methods or semi-analytical techniques. The author understands it as a safeguard in Monte Carlo simulation, where variance paths may otherwise become negative, but questions its relevance when a numerical grid explicitly restricts variance to positive values.

The text frames a modeling and numerical-method issue rather than providing an answer. It highlights the distinction between the model’s boundary behavior and the computational domain: restricting a grid does not by itself establish that the underlying variance process cannot reach zero or that boundary conditions are unaffected. No derivation, comparison of solvers, or empirical evidence is included, so the question alone does not settle whether the condition is mathematically required for each method.

Key ideas

  • The Feller condition is raised as a constraint on the Heston variance process.
  • The author contrasts possible negative variance in Monte Carlo simulation with a finite difference grid over positive variance values.
  • A positive computational grid does not, by itself, explain how the model behaves at the zero-variance boundary.
  • The document poses the numerical-method question but provides no answer or supporting results.

Tags

OptionsVolatilityDerivatives pricing
Full text
# Feller Condition in the Heston Model


# Feller Condition in the Heston Model












I understand that for MC simulations we require the Feller Condition otherwise the simulation becomes unstable when approximating the events when $v_t<0$, but for semi-analytical solution and using FDM, why is the Feller condition still required?

In the FDM case, you discretise $v \in (0,3)$, and the vol of vol will never bring $v<0$ anyway.

Then why in papers authors make sure the feller condition is satisfied when using FDM and semi-analytical solution when in reality it's not satisfied more often than not?

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.