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International Journal of Theoretical and Applied Finance· 2026Q2

Smile asymptotics for Bachelier implied volatility

Roberto Baviera, Michele Domenico Massaria

Short summary

This paper derives explicit expressions for Bachelier implied volatility tails, linking them to underlying return distribution decay and establishing a connection between characteristic function analyticity and smile slope.

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Abstract

We investigate the asymptotic behaviour of the Bachelier implied volatility tails, extending the large-strike results established for the Black-Scholes implied volatility. Exploiting the theory of regular variation, we derive explicit expressions for the Bachelier implied volatility in the wings of the smile, directly linking them to the tail decay of the underlying returns’ distribution. Furthermore, we establish a rigorous connection between the analyticity strip of the characteristic function and the asymptotic slope of the volatility smile. Moreover, we show that if the implied variance grows linearly for large absolute moneyness degree, the underlying returns’ distribution must exhibit exponential tail decay, and the corresponding characteristic function is analytic in a horizontal strip of the complex plane. These findings characterise valid models based solely on the observable asymptotic behaviour of the smile.

The authors' abstract, as published at the source. International Journal of Theoretical and Applied Finance, 2026 · DOI ↗

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Economics and EconometricsEconomics, Econometrics and Finance