Probability Distribution in the SABR Model of Stochastic Volatility

DOI10.1007/978-3-319-11605-1_1zbMath1418.91517OpenAlexW2186244866MaRDI QIDQ4560326

Patrick S. Hagan, Andrew Lesniewski, Diana E. Woodward

Publication date: 11 December 2018

Published in: Springer Proceedings in Mathematics & Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-11605-1_1

zbMATH Keywords

heat kernel expansionimplied volatilityWKB expansionSABRasymptotic smile formula

Mathematics Subject Classification ID

Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Derivative securities (option pricing, hedging, etc.) (91G20) Heat kernel (35K08)

Related Items (24)

Explicit density approximations for local volatility models using heat kernel expansions ⋮ Asymptotic Implied Volatility at the Second Order with Application to the SABR Model ⋮ Second Order Expansion for Implied Volatility in Two Factor Local Stochastic Volatility Models and Applications to the Dynamic $$\lambda $$-Sabr Model ⋮ General Asymptotics of Wiener Functionals and Application to Implied Volatilities ⋮ Approximate arbitrage-free option pricing under the SABR model ⋮ Options as silver bullets: valuation of term loans, inventory management, emissions trading and insurance risk mitigation using option theory ⋮ Dirichlet Forms and Finite Element Methods for the SABR Model ⋮ Reduction and reconstruction of stochastic differential equations via symmetries ⋮ Approximate solutions to second-order parabolic equations: evolution systems and discretization ⋮ A new algorithm for computing path integrals and weak approximation of SDEs inspired by large deviations and Malliavin calculus ⋮ Analytical approximation of the transition density in a local volatility model ⋮ Closed-form Arrow-Debreu pricing for the Hull-White short rate 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 ⋮ A VOLATILITY-OF-VOLATILITY EXPANSION OF THE OPTION PRICES IN THE SABR STOCHASTIC VOLATILITY MODEL ⋮ Precise asymptotics: robust stochastic volatility models ⋮ Hermite expansion of transition densities and European option prices for multivariate diffusions with jumps ⋮ Mild solutions to the dynamic programming equation for stochastic optimal control problems ⋮ Symmetrization associated with hyperbolic reflection principle ⋮ Bessel bridge representation for the heat kernel in hyperbolic space ⋮ Deep learning volatility: a deep neural network perspective on pricing and calibration in (rough) volatility models ⋮ Effective stochastic volatility: applications to ZABR-type models

Cites Work

• Perturbation methods in applied mathematics
• Stochastic calculus in manifolds. With an appendix by P.A. Meyer
• An upper bound to the spectrum of \(\Delta\) on a manifold of negative curvature
• DIFFUSION PROCESSES AND RIEMANNIAN GEOMETRY
• Transform Analysis and Asset Pricing for Affine Jump-diffusions
• Equivalent Black volatilities
• 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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