Choosing Local or Stochastic Volatility Models for Greeks

Summary

The document frames a model selection question for calculating option Greeks from a fitted volatility surface. It compares a local volatility model that matches the observed vanilla surface closely with a stochastic volatility model that may better represent market dynamics but has calibration error. It asks whether the closer fit or the potentially more realistic dynamics should carry greater weight when sensitivities are the goal.

The focus is on European claims and strategies whose values depend on the terminal distribution, including digitals and common option combinations. The author notes that the two model classes can produce different sensitivities even when both fit perfectly, and raises whether errors in surface regions of little interest matter. No answer, derivation, or empirical comparison is provided, so the document establishes the trade-off rather than resolving it; conclusions depend on the Greek being measured and the model's use case.

Key ideas

• A close local volatility fit to vanilla prices does not by itself establish accurate Greeks.
• Stochastic volatility may represent market dynamics differently while introducing calibration error.
• The two model classes can imply different sensitivities even when their price fits are both strong.
• For European claims, terminal-distribution fit is relevant, but the document does not determine which model gives better Greeks.

Tags

# Stochastic vs. local volatility model choices for greeks


# Stochastic vs. local volatility model choices for greeks












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.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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