Asymptotic Implied Volatility at the Second Order with Application to the SABR Model
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Publication:4560327
DOI10.1007/978-3-319-11605-1_2zbMath1418.91533arXiv0906.0658OpenAlexW2167560270MaRDI QIDQ4560327
Publication date: 11 December 2018
Published in: Springer Proceedings in Mathematics & Statistics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0906.0658
Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Derivative securities (option pricing, hedging, etc.) (91G20) Heat kernel (35K08)
Related Items (19)
Proof of non-convergence of the short-maturity expansion for the SABR model ⋮ ASYMPTOTICS OF THE TIME-DISCRETIZED LOG-NORMAL SABR MODEL: THE IMPLIED VOLATILITY SURFACE ⋮ On approximation of transition densities in calibration of 1-dimensional stochastic models of asset prices ⋮ Explicit density approximations for local volatility models using heat kernel expansions ⋮ Approximate arbitrage-free option pricing under the SABR model ⋮ A General Valuation Framework for SABR and Stochastic Local Volatility Models ⋮ Dirichlet Forms and Finite Element Methods for the SABR Model ⋮ Option pricing in the moderate deviations regime ⋮ MARKOVIAN STOCHASTIC VOLATILITY WITH STOCHASTIC CORRELATION — JOINT CALIBRATION AND CONSISTENCY OF SPX/VIX SHORT-MATURITY SMILES ⋮ Small-Time Asymptotics under Local-Stochastic Volatility with a Jump-to-Default: Curvature and the Heat Kernel Expansion ⋮ Analytical approximation of the transition density in a local volatility model ⋮ Mass at zero in the uncorrelated SABR model and implied volatility asymptotics ⋮ The survival probability of the SABR model: asymptotics and application ⋮ FUNCTIONAL ANALYTIC (IR-)REGULARITY PROPERTIES OF SABR-TYPE PROCESSES ⋮ On a one time-step Monte Carlo simulation approach of the SABR model: application to European options ⋮ The equivalent constant-elasticity-of-variance (CEV) volatility of the stochastic-alpha-beta-rho (SABR) model ⋮ Hermite expansion of transition densities and European option prices for multivariate diffusions with jumps ⋮ The principle of not feeling the boundary for the SABR model ⋮ Small-time asymptotics for Gaussian self-similar stochastic volatility models
Cites Work
- Heat kernel expansion: user's manual
- Computing the implied volatility in stochastic volatility models
- Analysis, Geometry, and Modeling in Finance
- Diffusion processes in a small time interval
- Probability Distribution in the SABR Model of Stochastic Volatility
- Asymptotics and calibration of local volatility models
- A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options
- Diffusion processes in a small time interval
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