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When Vanilla Skew Calibration Matters for Options Models

Article Quant Q&A · Author: Frido
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Summary

This note asks when an options model, particularly a stochastic local volatility model, needs to reproduce the observed vanilla implied volatility skew exactly. It suggests that close calibration matters when trading vanilla options and European products that can theoretically be replicated with vanillas, because their prices depend directly on the vanilla surface.

For exotic products whose exposure is mainly to forward or future volatility, the author is less certain that a perfect vanilla fit is necessary. The note raises the possibility of measuring how much fit quality matters, but gives no proposed metric, model comparison, data, or trading results. It is therefore a framing question rather than a worked method; it does not specify how to quantify replication error or account for model risk and calibration tradeoffs.

Key ideas

  • Vanilla option prices are directly linked to the implied volatility skew used to calibrate a model.
  • The author considers a close skew fit desirable for vanilla and theoretically vanilla-replicable European products.
  • The need for exact calibration is less clear for exotics driven mainly by forward or future volatility.
  • The note asks how to quantify the value of a better fit but supplies no measurement method or evidence.

Tags

OptionsVolatilityDerivatives pricing
Full text
# Options skew: when is a perfect fit desirable?


# Options skew: when is a perfect fit desirable?












I'm still troubled by a rather basic question, namely when is a perfect fit to the vanilla skew really necessary?

I think if you are trading vanilla options and/or Europeans that can in theory be perfectly replicated by vanillas (obviously) a `perfect' fit to the vanilla skew is desirable.

Other than that I'm not so sure there is an indisputable reason to have a model (read SLV) that gives a perfect fit? Especially for instance for more exotic products with exposure mainly to forward / future vol.

Is there a way to quantify my vagueness above?

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.