Brownian Path Generation and Polynomial Chaos

DOI10.1137/20M1343154zbMath1471.91567OpenAlexW3172464766MaRDI QIDQ4958391

Giray Ökten, Jamie Fox

Publication date: 8 September 2021

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

Full work available at URL: https://doi.org/10.1137/20m1343154

zbMATH Keywords

option pricingquasi-Monte Carloeffective dimensionpolynomial chaos expansionBrownian path generation

Mathematics Subject Classification ID

Numerical methods (including Monte Carlo methods) (91G60) Monte Carlo methods (65C05) Derivative securities (option pricing, hedging, etc.) (91G20) Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) (60J70)

Uses Software

• Manopt

Cites Work

• Unnamed Item
• The Pricing of Options and Corporate Liabilities
• How do path generation methods affect the accuracy of quasi-Monte Carlo methods for problems in finance?
• Fast orthogonal transforms and generation of Brownian paths
• Metamodelling with independent and dependent inputs
• Adaptive sparse polynomial chaos expansion based on least angle regression
• Interest rate models -- theory and practice. With smile, inflation and credit
• The Brownian bridge does not offer a consistent advantage in quasi-Monte Carlo integration
• Conditional Sampling for Barrier Option Pricing under the LT Method
• Good Path Generation Methods in Quasi-Monte Carlo for Pricing Financial Derivatives
• Manopt, a Matlab toolbox for optimization on manifolds
• Pricing Derivative Securities Using Integrated Quasi--Monte Carlo Methods with Dimension Reduction and Discontinuity Realignment
• Path Generation for Quasi-Monte Carlo Simulation of Mortgage-Backed Securities
• Generating Quasi-Random Paths for Stochastic Processes
• The Geometry of Algorithms with Orthogonality Constraints
• Optimization Techniques on Riemannian Manifolds
• The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
• Multidimensional Variation for Quasi-Monte Carlo
• Efficient Computation of Option Prices and Greeks by Quasi--Monte Carlo Method with Smoothing and Dimension Reduction
• Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates

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