As a follow-up of another question (which is I feel slightly separate, hence a new question). Assume we want to fit a volatility surface with the goal of calculating good greeks, not prices. We can choose between a SV or a LV model (SLV is a very distant but also possible choice). Now assume that
- We manage to find a very good fit for a LV model.
- We choose some SV model and calibrate it to our vanilla surface, but have some calibration error (tricky add-on: in areas of the surface we currently don't care about - does that change the situation?)
The question is: which of these two model choices is a better choice for greeks? One one hand, I know that a SV model might approximate the true dynamics of my market a bit better, even if not perfectly, on the other hand the LV model matches the prices in that market better. I can of course "just calculate the sensitivities" but they will differ (even if both fits were perfect). From what I see, LV models produce wrong sensitivities (that's why SABR came into play) but it must be worth something that the SV model has calibration errors, right?
To make it even more difficult, focus on European-style securities like digitals or option strategies like risk reversals, straddles, iron condors, etc., so securities that really just depend on the terminal distribution - which should be fit well by the LV model.