Pricing Options under Rough Volatility with Backward SPDEs

DOI10.1137/20M1357639zbMath1484.91469arXiv2008.01241OpenAlexW4221040644MaRDI QIDQ5065084

Yao Yao, Christian Bayer, Jinniao Qiu

Publication date: 18 March 2022

Published in: SIAM Journal on Financial Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2008.01241

zbMATH Keywords

option pricingstochastic partial differential equationmachine learningstochastic Feynman-Kac formularough volatilitystochastic Black-Scholes equation

Mathematics Subject Classification ID

Numerical methods (including Monte Carlo methods) (91G60) Stopping times; optimal stopping problems; gambling theory (60G40) Derivative securities (option pricing, hedging, etc.) (91G20) Stochastic partial differential equations (aspects of stochastic analysis) (60H15)

Related Items

American Options in the Volterra Heston Model ⋮ Deep Curve-Dependent PDEs for Affine Rough Volatility ⋮ An overview on deep learning-based approximation methods for partial differential equations

Cites Work

• \(L ^{p }\) theory for super-parabolic backward stochastic partial differential equations in the whole space
• On the quasi-linear reflected backward stochastic partial differential equations
• Affine fractional stochastic volatility models
• Asymptotic analysis for stochastic volatility: martingale expansion
• Adapted solution of a backward stochastic differential equation
• On the Itô--Wentzell formula for distribution-valued processes and related topics
• A duality analysis on stochastic partial differential equations
• Reflected solutions of backward SDE's, and related obstacle problems for PDE's
• Multilayer feedforward networks are universal approximators
• The microstructural foundations of leverage effect and rough volatility
• On semi-linear degenerate backward stochastic partial differential equations
• Affine Volterra processes
• A martingale approach for fractional Brownian motions and related path dependent PDEs
• Weak solution for a class of fully nonlinear stochastic Hamilton-Jacobi-Bellman equations
• On the martingale property in the rough Bergomi model
• On viscosity solutions of path dependent PDEs
• On the short-time behavior of the implied volatility for jump-diffusion models with stochastic volatility
• Local martingales, bubbles and option prices
• OPTIMAL TRADE EXECUTION UNDER GEOMETRIC BROWNIAN MOTION IN THE ALMGREN AND CHRISS FRAMEWORK
• Stochastic Differential Games and Viscosity Solutions of Hamilton–Jacobi–Bellman–Isaacs Equations
• Adapted solution of a backward semilinear stochastic evolution equation
• Stochastic Hamilton–Jacobi–Bellman Equations
• Backward Stochastic Differential Equations in Finance
• Volatility is rough
• Viscosity Solutions of Stochastic Hamilton--Jacobi--Bellman Equations
• Pricing American options by exercise rate optimization
• Deep backward schemes for high-dimensional nonlinear PDEs
• Solving high-dimensional partial differential equations using deep learning
• Machine learning for pricing American options in high-dimensional Markovian and non-Markovian models
• Pricing under rough volatility
• Stochastic Equations in Infinite Dimensions
• A FIRST‐ORDER BSPDE FOR SWING OPTION PRICING
• The characteristic function of rough Heston models
• A regularity structure for rough volatility
• Stochastic differential equations. An introduction with applications.