Heston Call Pricing Boundary When Variance Reaches Zero

Summary

The document asks why the Heston model’s call-price boundary at zero instantaneous variance equals the discounted intrinsic value of the option. It defines the option value as a function of time, spot price, and variance, then presents the boundary condition without an explanation or answer.

The underlying idea is that when variance is zero, the model’s stochastic volatility component disappears at that boundary, so the stock follows deterministic risk-neutral growth until expiry. Discounting the expected terminal call payoff gives the stated expression. The source itself provides no derivation, assumptions, or supporting evidence, so it is best read as a narrowly framed question rather than a complete treatment. In particular, the boundary interpretation depends on the Heston dynamics and pricing assumptions; the document does not discuss how the variance process behaves at zero or broader option-pricing implications.

Key ideas

• The document asks about the call-price boundary in the Heston stochastic-volatility model when variance is zero.
• It states the boundary value as discounted intrinsic value at the current spot price.
• The question provides no derivation or answer, leaving the model assumptions and boundary behavior unexplored.

Tags

# how to understand the zero vol condition in Heston stochastic vol model


# how to understand the zero vol condition in Heston stochastic vol model












I can't understand one of the boundary conditions in Heston's model: $$c(t,s,0) = (s-e^{-r(T-t)}K)^+$$ Why the current vol is zero can deduce such result. here $c(t,s,v)$ $s$ is current price and $v$ is current vol.

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