Fine-tune your smile: Correction to Hagan et al

Details Fine-tune your smile: Correction to Hagan et al Fine-tune your smile: Correction to Hagan et al

2007-08-07

arxiv.org/abs/0708.0998v3

Economy

Quantitative Finance

Computational Finance

Typos and reference corrected. Eq (3) valid for all x now

Scientific paper

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 $\beta\to 1$. Furthermore, numerical simulations show
that it reduces or eliminates known pathologies of the earlier formula.

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