Asymptotics of implied volatility to arbitrary order

DOI10.1007/s00780-013-0223-6zbMath1307.91175OpenAlexW4375905808MaRDI QIDQ468415

J. Herrera, Sumit K. Garg

Publication date: 7 November 2014

Published in: Finance and Stochastics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00780-013-0223-6

zbMATH Keywords

asymptoticsimplied volatility

Mathematics Subject Classification ID

Stochastic models in economics (91B70) Derivative securities (option pricing, hedging, etc.) (91G20)

Related Items (42)

EXPLICIT IMPLIED VOLATILITIES FOR MULTIFACTOR LOCAL‐STOCHASTIC VOLATILITY MODELS ⋮ Large deviations for the extended Heston model: the large-time case ⋮ Large and moderate deviations for stochastic Volterra systems ⋮ ASYMPTOTICS OF THE TIME-DISCRETIZED LOG-NORMAL SABR MODEL: THE IMPLIED VOLATILITY SURFACE ⋮ SHORT MATURITY ASIAN OPTIONS FOR THE CEV MODEL ⋮ Large Deviation Principle for Volterra Type Fractional Stochastic Volatility Models ⋮ Short-term asymptotics for the implied volatility skew under a stochastic volatility model with Lévy jumps ⋮ Black-Scholes in a CEV random environment ⋮ Implied Volatility of Basket Options at Extreme Strikes ⋮ Short-dated smile under rough volatility: asymptotics and numerics ⋮ Closed-form implied volatility surfaces for stochastic volatility models with jumps ⋮ Gaussian stochastic volatility models: scaling regimes, large deviations, and moment explosions ⋮ Option pricing in the moderate deviations regime ⋮ Asymptotic behavior and calibration of short-time option prices under the normal tempered stable model ⋮ Uniform Bounds for Black--Scholes Implied Volatility ⋮ Short Maturity Asian Options in Local Volatility Models ⋮ Small‐time, large‐time, and asymptotics for the Rough Heston model ⋮ Extreme-strike asymptotics for general Gaussian stochastic volatility models ⋮ SUBLEADING CORRECTION TO THE ASIAN OPTIONS VOLATILITY IN THE BLACK–SCHOLES MODEL ⋮ AN EXPLICIT IMPLIED VOLATILITY FORMULA ⋮ Small-time moderate deviations for the randomised Heston model ⋮ W-shaped implied volatility curves and the Gaussian mixture model ⋮ Asymptotics for Rough Stochastic Volatility Models ⋮ EFFECTIVE ASYMPTOTICS ANALYSIS FOR FINANCE ⋮ Analytical approximation of the transition density in a local volatility model ⋮ Shapes of Implied Volatility with Positive Mass at Zero ⋮ The large-maturity smile for the Stein-Stein model ⋮ Short-Time Expansions for Call Options on Leveraged ETFs Under Exponential Lévy Models with Local Volatility ⋮ Precise asymptotics: robust stochastic volatility models ⋮ The asymptotic smile of a multiscaling stochastic volatility model ⋮ HIGH‐ORDER SHORT‐TIME EXPANSIONS FOR ATM OPTION PRICES OF EXPONENTIAL LÉVY MODELS ⋮ The Randomized Heston Model ⋮ Marginal Density Expansions for Diffusions and Stochastic Volatility II: Applications ⋮ Asymptotics for volatility derivatives in multi-factor rough volatility models ⋮ Large-maturity regimes of the Heston forward smile ⋮ Asymptotic behaviour of randomised fractional volatility models ⋮ General Smile Asymptotics with Bounded Maturity ⋮ Short-time near-the-money skew in rough fractional volatility models ⋮ Small-time asymptotics for Gaussian self-similar stochastic volatility models ⋮ Asymptotic Analysis of Stock Price Densities and Implied Volatilities in Mixed Stochastic Models ⋮ Asymptotics of Forward Implied Volatility ⋮ Short-time expansions for close-to-the-money options under a Lévy jump model with stochastic volatility

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