Fine-tune your smile: Correction to Hagan et al
Abstract
Description
In this small note we use results derived in Berestycki et al. to correct the celebrated formulae of Hagan et al. We derive explicitly the correct zero order term in the expansion of the implied volatility in time to maturity. The new term is consistent as $β\to 1$. Furthermore, numerical simulations show that it reduces or eliminates known pathologies of the earlier formula.
Typos and reference corrected. Eq (3) valid for all x now
Typos and reference corrected. Eq (3) valid for all x now