Fine-tune your smile: Correction to Hagan et al

2007/08/07 by Jan Obloj, Obloj, Jan · 1 citation
Economics, Econometrics and Finance · Mathematics · #Computational Finance (q-fin.CP) #FOS: Economics and business #FOS: Mathematics #Probability (math.PR) #Statistical Finance (q-fin.ST) #math.PR #q-fin.CP #q-fin.ST

paper · pdf · doi:10.48550/arxiv.0708.0998

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

arxiv created 2008/03/18 · arxiv updated 2009/12/01

Abstract

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→ 1. Furthermore, numerical simulations show that it reduces or eliminates known pathologies of the earlier formula.

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