# 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

• To confuse you a bit more: there is 'in-model' vega and 'out-model' vega. The former is a definition of vega consistent with the model. In stoch vol models such as Heston the correct definition would be indeed to bump $v_0$. The latter is however you want to define vega. Some calculate vega as the BS vega (i.e. wrt to implied vol), others maybe wrt to the variance swap strike, or something else. The reason 'out-of-model' vega is popular is because nobody really believes eg Heston, and out of model vega could make it easier to vega hedge. Feb 14 at 12:47
• What pricer in BBG? OVME, OVML, DLIB? If I look at OVML, I would say vega of the Heston model as implemented is very questionable. BS, LV, SLV and SV all provide similar answers for vega for a vanilla option. If I manually bump the entire vol surface by 1% and reprice (hence recalibrate) with that new vol surface, I get a change in line with all other vega values. Feb 15 at 11:26