A NEW LOOK AT SHORT-TERM IMPLIED VOLATILITY IN ASSET PRICE MODELS WITH JUMPS

DOI10.1111/mafi.12055zbMath1403.91348arXiv1207.0843OpenAlexW2161673224MaRDI QIDQ2788693

Peter Tankov, Aleksandar Mijatović

Publication date: 22 February 2016

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

Full work available at URL: https://arxiv.org/abs/1207.0843

zbMATH Keywords

asymptotic behaviorLévy measureimplied volatilityBlumenthal-Getoor indexexponential Lévy modelsput-call symmetryexponential strikeLévy process with jumps of (finite) infinite variationslog-strikeshort-dated options

Mathematics Subject Classification ID

Related Items (28)

Asymptotic Behavior of the Fractional Heston Model ⋮ Short-term asymptotics for the implied volatility skew under a stochastic volatility model with Lévy jumps ⋮ Black-Scholes in a CEV random environment ⋮ Short-time at-the-money skew and rough fractional volatility ⋮ Implied Volatility of Basket Options at Extreme Strikes ⋮ Option pricing in the moderate deviations regime ⋮ Asymptotic behavior and calibration of short-time option prices under the normal tempered stable model ⋮ Simulation of the drawdown and its duration in Lévy models via stick-breaking Gaussian approximation ⋮ Small‐time, large‐time, and asymptotics for the Rough Heston model ⋮ Small-time moderate deviations for the randomised Heston model ⋮ The economics of time as it is embedded in the prices of options§ ⋮ Asymptotics for Rough Stochastic Volatility Models ⋮ Analytical approximation of the transition density in a local volatility model ⋮ Testing and inference for fixed times of discontinuity in semimartingales ⋮ Correction to Black--Scholes Formula Due to Fractional Stochastic Volatility ⋮ Third-order short-time expansions for close-to-the-money option prices under the CGMY model ⋮ The asymptotic smile of a multiscaling stochastic volatility model ⋮ The Randomized Heston Model ⋮ Option pricing under fast‐varying long‐memory stochastic volatility ⋮ Extreme at-the-money skew in a local volatility model ⋮ Large-maturity regimes of the Heston forward smile ⋮ Nonparametric spot volatility from options ⋮ 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 ⋮ Asymptotics of Forward Implied Volatility ⋮ Rough volatility and CGMY jumps with a finite history and the Rough Heston model – small-time asymptotics in the regime ⋮ Short-time expansions for close-to-the-money options under a Lévy jump model with stochastic volatility

Cites Work

• Estimating the degree of activity of jumps in high frequency data
• Spectral estimation of the fractional order of a Lévy process
• Asymptotic Formulas with Error Estimates for Call Pricing Functions and the Implied Volatility at Extreme Strikes
• Small-Time Asymptotics of Option Prices and First Absolute Moments
• Asymptotics of Implied Volatility far from Maturity
• REGULAR VARIATION AND SMILE ASYMPTOTICS
• THE MOMENT FORMULA FOR IMPLIED VOLATILITY AT EXTREME STRIKES
• The Small-Maturity Smile for Exponential Lévy Models
• ON THE RELATIONSHIP BETWEEN THE CALL PRICE SURFACE AND THE IMPLIED VOLATILITY SURFACE CLOSE TO EXPIRY
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