Asymptotic Formulas with Error Estimates for Call Pricing Functions and the Implied Volatility at Extreme Strikes

TL;DR

This paper derives precise asymptotic formulas with error bounds for call pricing functions and implied volatility at extreme strikes, connecting to established tail-wing formulas and analyzing specific stochastic models.

Contribution

It introduces new asymptotic formulas with error estimates for implied volatility and call prices, extending existing tail-wing formulas to several stochastic models.

Findings

Asymptotic formulas with error estimates for implied volatility at extreme strikes.

Validation of formulas against Lee’s moment formulas and tail-wing formulas.

Application to Hull-White, Stein-Stein, and Heston models.

Abstract

In this paper, we obtain asymptotic formulas with error estimates for the implied volatility associated with a European call pricing function. We show that these formulas imply Lee's moment formulas for the implied volatility and the tail-wing formulas due to Benaim and Friz. In addition, we analyze Pareto-type tails of stock price distributions in uncorrelated Hull-White, Stein-Stein, and Heston models and find asymptotic formulas with error estimates for call pricing functions in these models.