In Friz et al. [Precise asymptotics for robust stochastic volatility models. Ann. Appl. Probab, 2021, 31(2), 896-940], we introduce a new methodology to analyze large classes of (classical and rough) stochastic volatility models, with special regard to short-time and small-noise formulae for option prices, using the framework [Bayer et al., A regularity structure for rough volatility. Math. Finance, 2020, 30(3), 782-832]. We investigate here the fine structure of this expansion in large deviations and moderate deviations regimes, together with consequences for implied volatility. We discuss computational aspects relevant for the practical application of these formulas. We specialize such expansions to prototypical rough volatility examples and discuss numerical evidence.

Friz, P.k., Gassiat, P., Pigato, P. (2022). Short-dated smile under rough volatility: asymptotics and numerics. QUANTITATIVE FINANCE, 22(3), 463-480 [10.1080/14697688.2021.1999486].

Short-dated smile under rough volatility: asymptotics and numerics

Pigato P.
2022-01-01

Abstract

In Friz et al. [Precise asymptotics for robust stochastic volatility models. Ann. Appl. Probab, 2021, 31(2), 896-940], we introduce a new methodology to analyze large classes of (classical and rough) stochastic volatility models, with special regard to short-time and small-noise formulae for option prices, using the framework [Bayer et al., A regularity structure for rough volatility. Math. Finance, 2020, 30(3), 782-832]. We investigate here the fine structure of this expansion in large deviations and moderate deviations regimes, together with consequences for implied volatility. We discuss computational aspects relevant for the practical application of these formulas. We specialize such expansions to prototypical rough volatility examples and discuss numerical evidence.
2022
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore SECS-S/06 - METODI MATEMATICI DELL'ECONOMIA E DELLE SCIENZE ATTUARIALI E FINANZIARIE
Settore SECS-P/05 - ECONOMETRIA
English
Rough volatility
European option pricing
Implied volatility
Small-time asymptotics
Rough paths
Regularity structures
Karhunen-Loeve
Friz, P.k., Gassiat, P., Pigato, P. (2022). Short-dated smile under rough volatility: asymptotics and numerics. QUANTITATIVE FINANCE, 22(3), 463-480 [10.1080/14697688.2021.1999486].
Friz, Pk; Gassiat, P; Pigato, P
Articolo su rivista
File in questo prodotto:
File Dimensione Formato  
2009.08814.pdf

solo utenti autorizzati

Tipologia: Documento in Pre-print
Licenza: Non specificato
Dimensione 547.93 kB
Formato Adobe PDF
547.93 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/285057
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 7
  • ???jsp.display-item.citation.isi??? 7
social impact