I am given a plot of the fair value of a complex derivative against a scenario spot shift for a range odd possible shifts (-40% to 40%). Let us say the pricing model is a local vol model. I am unable to understand the underlying mechanism of the 'shift'. Here is my understanding of the mechanism:
a. The model calibrates its local volatility function to the observable market for the current spot trading in the market (say 100). This way it can reproduce the vanilla portfolio as it exists in the market today.
b. Now upon the spot shift, the model assumes that the spot is different, say 120. But there does not exist a volatility surface in the market for a spot of 120 (unless one interpolates in log-moneyness?); what does the model calibrate to? Or does it assume the same local volatility function as in (a)?