Vega Sensitivity in the Heston Model

Summary

The document raises a practical question about estimating European option vega under the Heston stochastic volatility model. The author reports computing delta and gamma by bumping spot and recalculating prices or delta, with results matching Bloomberg values. For vega, the author bumps the initial variance and observes an estimate they believe is too low, noting that the long-run variance mean also affects the model’s dynamics.

No answer or calculation method is included, so the document does not establish which Heston parameter bump should define vega or how to compare it with a market quote. The question highlights that a sensitivity must specify which input is perturbed, but it gives no evidence resolving whether vega should be measured through initial variance, long-run mean, volatility, or another calibration convention. Its results are the author’s report, not independently documented validation.

Key ideas

• The author estimates delta and gamma by bumping spot and recalculating option values or delta.
• The document questions whether bumping only initial variance captures vega in the Heston model.
• Long-run mean variance is identified as another model parameter relevant to the concern.
• The text contains no answer or specified vega bump convention.

Tags

# How to compute Vega in the Heston Model


# How to compute Vega in the Heston Model












I am computing European Option Sensitivity as: Delta, Vega and Gamma. I am using Heston Model to simulation spot and the variance.

While computing Delta and Gamma, I understand, we need to bump spot by 1 unit and re-compute option price(for delta) and delta(for gamma) respectively. My results matched with the Bloomberg delta and gamma values.

However, for computation of vega, what else needs to be bumped other than initial variance(v0) since vega is a function of theta(long term mean of variance) as well. If I just bump initial variance(v0) and re-compute the option price, my vega is underestimated.

I was also referring to the similar question: Vega in the Heston model, but it doesn't provides any specific answer

Any help is appreciated.

Thanks -Garv

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