Comparing Market Implied Volatility with Dupire Local Volatility

Summary

The document poses a modeling question about whether local volatility derived from an observed implied volatility surface reproduces that surface or changes its skew. It outlines a workflow: obtain market implied volatilities, fit a model such as SVI, use the fitted surface with the Dupire equation to derive local volatility, price options under that local volatility, and convert their prices back into implied volatilities.

The central issue is whether the resulting implied volatilities should match the original market values closely, and whether local volatility flattens the existing skew faster. The document provides no derivation, numerical experiment, or answer, so it establishes a question rather than a conclusion. Any comparison would depend on how the surface is fitted and how the local-volatility pricing and implied-volatility recovery are carried out; those details are not specified.

Key ideas

• A proposed workflow derives local volatility from a fitted market implied volatility surface using Dupire’s equation.
• The resulting local-volatility prices can be converted back into implied volatilities for comparison.
• The document asks whether this process preserves the market surface and its skew but supplies no answer or evidence.

Tags

# Implied volatility from local volatility versus market implied volatility


# Implied volatility from local volatility versus market implied volatility












Does the local volatility flattens the (existing not forward) skew faster than what we observed in the implied volatility surface?

The process is:

- Get market implied volatilities

- Fit a IV model (i.e. SVI)

- Using IVs and Dupire equation obtain LV, price options and imply IV from those options.

What would you observe? Assuming that 1 matches close 2, and 3 is derived using Dupire equation from 2, would you expect to have 3 matching very closely 1 (or 2)?

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