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

  1. We manage to find a very good fit for a LV model.
  2. 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.

  • $\begingroup$ I don't think any of the structures requires or warrants a model different from Black Scholes because they are all just combinations of simply European options. SLV isn't very distant either, because any SLV model can be made a SV or LV model by simply choosing the appropriate mixing fraction. $\endgroup$
    – AKdemy
    Jul 24, 2022 at 22:35
  • 1
    $\begingroup$ Agreed with AKdemy. Be careful though: even if your goal is to manage vanilla books (claims that depend on terminal distribution only, i.e. the statics of a model), by dynamically delta-hedging, you will expose yourself back to how the spot versus implied volatility surface evolve together (i.e. the dynamics of a model). Each model will provide its own break-even levels. If you trust these, use that model. If not, use BS and add your own view by trading in some shadow delta (see quant.stackexchange.com/questions/25244/…). $\endgroup$
    – Quantuple
    Jul 25, 2022 at 6:53
  • $\begingroup$ @AKdemy see that's where it starts - the BS Delta already ignores the skew. if this was an FX product and the smile was a lot more symmetric, I'd even have multiple skews there. That's my issue there - I'm not talking about pricing (LV is enough if I don't have traded strikes, otherwise, BS) but this is about the greeks which DO differ between models, even if fit is perfect for both. $\endgroup$
    – freistil90
    Jul 25, 2022 at 7:15
  • $\begingroup$ @Quantuple thanks, saw that later that evening, that actually summarizes some parts of my concern - essentially I think my question boils down how bad model misspecifications are if I hit the dynamics better vs. hitting prices but having worse dynamics models. The last part there seems to actually answer parts of that - thanks! $\endgroup$
    – freistil90
    Jul 25, 2022 at 7:19


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