Extrapolating Dupire Local Volatility at Extreme Strikes

Summary

This document focuses on how implied volatility extrapolation affects Dupire local volatility estimates at strikes beyond those observed in the market. A typical implementation first fits a smooth representation of the implied volatility surface, then derives local volatility from the associated call price surface. Because market data do not cover extreme strike regions, the fitted surface must be extended there, and that choice can affect the model’s behavior.

The paper offers direct analytical insights into the asymptotic behavior of local volatility at extreme strikes. Its stated contribution is to examine local volatility itself in those regimes, alongside prior work on implied volatility extrapolation. The excerpt does not provide the specific asymptotic formulas, assumptions, or empirical tests, so readers would need the full paper to assess implementation details or determine which extrapolation choices are robust in practice.

Key ideas

• Dupire local volatility is derived from a call price surface built from implied volatility data.
• A typical workflow fits a smooth implied volatility surface before computing local volatility.
• Extrapolation at extreme strikes matters because those regions are not represented in observed market data.
• The paper gives analytical insights into the asymptotic behavior of local volatility at extreme strikes.
• The excerpt does not state the formulas, assumptions, or validation results.

Tags

# Don't stay local - extrapolation analytics for Dupire's local volatility


# Don't stay local - extrapolation analytics for Dupire's local volatility









A robust implementation of a Dupire type local volatility model is an important issue for every option trading floor. Typically, this (inverse) problem is solved in a two step procedure : (i) a smooth parametrization of the implied volatility surface; (ii) computation of the local volatility based on the resulting call price surface. Point (i), and in particular how to extrapolate the implied volatility in extreme strike regimes not seen in the market, has been the subject of numerous articles, starting with Lee (Math. Finance, 2004). In the present paper we give direct analytic insights into the asymptotic behavior of local volatility at extreme strikes.

Shown in full with attribution under the source's licence. Licence: abstract CC0

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