On the Bachelier implied volatility at extreme strikes

TL;DR

This paper explores the behavior of Bachelier (Normal) implied volatility at extreme strikes, analyzing arbitrage constraints and implications for implied volatility extrapolation.

Contribution

It investigates the growth limits of Bachelier implied volatility at extreme strikes, extending Lee's results from the Black-Scholes model.

Findings

Bachelier implied volatility cannot grow faster than linearly in log-moneyness.

Analysis of arbitrage constraints on vanilla options.

Insights into appropriate extrapolation methods for implied volatility at extremes.

Abstract

What kind of implied volatility extrapolation is appropriate? Roger Lee proved that the Black-Scholes implied variance can not grow faster than linearly in log-moneyness. This paper investigates what happens in the Bachelier (or Normal) implied volatility world, making sure to cover the various aspects of vanilla option arbitrages.