General smile asymptotics with bounded maturity

TL;DR

This paper derives precise asymptotic formulas for implied volatility smiles under various regimes by analyzing risk-neutral log-return distributions, extending prior results to include models like Heston and jump diffusions.

Contribution

It provides explicit conditions on log-return distributions that lead to sharp implied volatility asymptotics across multiple regimes, broadening the scope of previous analyses.

Findings

Derived explicit asymptotic estimates for implied volatility.

Extended previous work to include models like Heston and jump diffusions.

Applicable to a variety of popular financial models.

Abstract

We provide explicit conditions on the distribution of risk-neutral log-returns which yield sharp asymptotic estimates on the implied volatility smile. We allow for a variety of asymptotic regimes, including both small maturity (with arbitrary strike) and extreme strike (with arbitrary bounded maturity), extending previous work of Benaim and Friz [Math. Finance 19 (2009), 1-12]. We present applications to popular models, including Carr-Wu finite moment logstable model, Merton's jump diffusion model and Heston's model.