Short-dated smile under rough volatility: asymptotics and numerics

DOI10.1080/14697688.2021.1999486zbMath1487.91137arXiv2009.08814OpenAlexW3087046624MaRDI QIDQ5072906

Peter K. Friz, Paul Gassiat, Paolo Pigato

Publication date: 5 May 2022

Published in: Quantitative Finance (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2009.08814

zbMATH Keywords

small-time asymptoticsimplied volatilityrough pathsEuropean option pricingregularity structuresKarhunen-Loeverough volatility

Mathematics Subject Classification ID

Derivative securities (option pricing, hedging, etc.) (91G20)

Related Items

On the Discrete-Time Simulation of the Rough Heston Model, Empirical analysis of rough and classical stochastic volatility models to the SPX and VIX markets, Approximation of Stochastic Volterra Equations with kernels of completely monotone type, Local volatility under rough volatility

Cites Work

• Unnamed Item
• Unnamed Item
• Asymptotics of implied volatility to arbitrary order
• Asymptotic analysis for stochastic volatility: martingale expansion
• The microstructural foundations of leverage effect and rough volatility
• Laplace approximation for rough differential equation driven by fractional Brownian motion
• Time-inhomogeneous Gaussian stochastic volatility models: large deviations and super roughness
• Gaussian stochastic volatility models: scaling regimes, large deviations, and moment explosions
• Precise asymptotics: robust stochastic volatility models
• A note on ergodic transformations of self-similar Volterra Gaussian processes
• On the short-time behavior of the implied volatility for jump-diffusion models with stochastic volatility
• Asymptotics for Rough Stochastic Volatility Models
• Computing the implied volatility in stochastic volatility models
• The Malliavin Calculus and Related Topics
• Gaussian Hilbert Spaces
• Short-time at-the-money skew and rough fractional volatility
• General Asymptotics of Wiener Functionals and Application to Implied Volatilities
• Option pricing in the moderate deviations regime
• Pathwise large deviations for the rough Bergomi model
• Turbocharging Monte Carlo pricing for the rough Bergomi model
• The Small-Time Smile and Term Structure of Implied Volatility under the Heston Model
• Short-Term At-the-Money Asymptotics under Stochastic Volatility Models
• Machine learning for pricing American options in high-dimensional Markovian and non-Markovian models
• Pricing under rough volatility
• Volatility has to be rough
• Hierarchical adaptive sparse grids and quasi-Monte Carlo for option pricing under the rough Bergomi model
• Log-Modulated Rough Stochastic Volatility Models
• Short-time near-the-money skew in rough fractional volatility models
• On the Curvature of the Smile in Stochastic Volatility Models
• Fractional Brownian Motions, Fractional Noises and Applications
• The characteristic function of rough Heston models
• A regularity structure for rough volatility
• Hybrid scheme for Brownian semistationary processes