Questions on Interpolating and Extrapolating Local Volatility

Summary

The document raises practical questions about constructing a local volatility surface from call prices using Dupire’s formula. It considers a bounded region of strike and maturity values and asks whether interpolation should be performed on the derivatives of call prices before calculating local volatility, or directly on the volatility surface itself.

For values outside the observed region, it asks whether holding all call price derivatives constant is a reasonable extrapolation assumption. The document provides no answers, method comparison, evidence, or discussion of arbitrage constraints and boundary behavior. It therefore serves as a narrowly framed problem statement about surface construction rather than guidance on how to implement or validate an interpolation or extrapolation scheme.

Key ideas

• Dupire’s formula relates local volatility to derivatives of call prices.
• The document asks whether interpolation should be applied to call price derivatives or directly to local volatility.
• It questions whether constant call price derivatives are a sound assumption beyond the observed strike and maturity region.
• No method, evidence, or resolution to these questions is provided.

Tags

# how to interpolate and extrapolate the local volatility surface?


# how to interpolate and extrapolate the local volatility surface?












Local volatility can be computed in terms of call prices using Dupire's formula. Assume we have a rectangle call price surface, let's say $I = [30,60]\times[1 day, 1year]$.

For interpolation, should we interpolate the derivatives of call prices and compute the local volatility instead of directly interpolate the local volatility surface?

For extrapolation, should we assume all the derivatives of the call prices be constant if strike or tenor are outside $I$?

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.