How to quantify Vega PNL from volatility moving along a steep moneyness surface when bucket Vega shows zero?

Based on this answer : Question : When the implied volatility surface remains identical over two consecutive days, my current Vega P&L calculation yields zero. However, market movements cause options' effective volatility to shift along the surface—particularly impactful with steep volatility skew. How should we properly quantify this P&L component? Current methodology : Discretized volatility surface at $t$ : $\sigma_{ij}^t$ (moneyness $i$ , term $j$ ) $\Delta \sigma_{ij} \equiv \sigma_{ij}^{t+1} - \sigma_{ij}^{t}$ (matrix subtraction) Bucket Vega calculation: $\small\text{BucketVega}_{ij} = \left[PV(\sigma_{ij} + 0.01) - PV(\sigma_{ij})\right] \times 100$ Vega P&L $= \sum_i \sum_j \left( \text{BucketVega}_{ij} \times \Delta \sigma_{ij} \right)$ Conflict under sticky delta : Spot moves shift options to new moneyness coordinates → effective IV changes due to skew Identical surfaces give $\Delta \sigma_{ij} = 0$ → skew-induced P&L vanishes! (Example: ATM call becomes OTM and "slides" to lower vol point on static surface) Required quantification : How to capture P&L from: Movement along static surface (skew effect) Time-decay (roll-down $\partial\sigma/\partial\tau$ ) True surface shape changes