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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)?

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  • $\begingroup$ This boils down to „sticky strike vs sticky delta“. There exists a nice explanation by Derman: emanuelderman.com/wp-content/uploads/2013/09/smile-lecture9.pdf . IIRC, it depends on the market which rule to use. $\endgroup$ Jul 28, 2021 at 4:10
  • $\begingroup$ I understand. So there is no concept of recalibration upon a spot shift, one just takes the same parameters as it had calibrated to the observable vanilla market? $\endgroup$
    – Arshdeep
    Jul 28, 2021 at 9:26
  • $\begingroup$ Hi, this is not my core area of expertise, maybe somebody else can chime in: To my understanding, you can either 1) move the spot point on the volatility surface, e.g. you apply a shifted volatility surface relative to the old point; or 2) move the whole surface as well, i.e. the spot is unchanged, relative to the surface. In any case, I think you do not need to recalibrate the surface. You can find some discussion on this topic here on QSE as well, e.g.: quant.stackexchange.com/questions/44248/… $\endgroup$ Jul 28, 2021 at 10:03
  • $\begingroup$ I agree with the discussion above. Forget you are pricing a complex derivative and assume you are pricing a vanilla option instead, what would happen then? It is indeed a question of how you effectively compute the delta, i.e. what are the "state variables" (here the spot) of your model versus what are the fixed "parameters" (fixed local vol function vs. fixed vanilla prices & stripping on the fly). This is what I tried to allude to in quant.stackexchange.com/questions/25244/…, but Bergomi has a whole chapter about LV delta (and its ambiguity) $\endgroup$
    – Quantuple
    Jul 30, 2021 at 6:03

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