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

作者：Gulisashvili Archil^*

来源：SIAM Journal on Financial Mathematics, 2010, 1(1): 609-641.

DOI：10.1137/090762713

• call and put pricing functions
• implied volatility
• asymptotic formulas
• Pareto-type distributions
• regularly varying functions

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.

• 出版日期2010