Intermediate rank lattice rules and applications to finance

DOI10.1016/j.apnum.2007.11.024zbMath1161.65003OpenAlexW2078698791MaRDI QIDQ960285

Yongzeng Lai

Publication date: 16 December 2008

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2007.11.024

zbMATH Keywords

Riemann zeta functionconvergenceoption pricingMonte Carlo methoderror boundquadraturelow-discrepancy point setsquasi-Monte Carlo methodcomputational financeSobol' sequencesgood lattice rulehigh dimensional numerical integrationintermediate rank lattice rulesKorbov type lattice rulesmaximum rank rule

Mathematics Subject Classification ID

Numerical methods (including Monte Carlo methods) (91G60) Monte Carlo methods (65C05) Irregularities of distribution, discrepancy (11K38) Pseudo-random numbers; Monte Carlo methods (11K45)

Related Items (5)

Efficient simulation of Greeks of multiasset European and Asian style options by Malliavin calculus and quasi-Monte Carlo methods ⋮ Expected integration approximation under general equal measure partition ⋮ SIMULATION OF MULTI-ASSET OPTION GREEKS UNDER A SPECIAL LÉVY MODEL BY MALLIAVIN CALCULUS ⋮ Valuation on an outside-reset option with multiple resettable levels and dates ⋮ Generating inverse Gaussian random variates by approximation

Uses Software

• QSIMVN

Cites Work

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• Existence of good lattice points in the sense of Hlawka
• Tractability of multivariate integration for weighted Korobov classes
• Component-by-component construction of good lattice rules with a composite number of points
• Error bounds for rank 1 lattice quadrature rules modulo composites
• Component-by-component construction of good lattice rules
• On the use of low discrepancy sequences in Monte Carlo methods
• On the step-by-step construction of quasi--Monte Carlo integration rules that achieve strong tractability error bounds in weighted Sobolev spaces
• Parameters for Integrating Periodic Functions of Several Variables
• Fast algorithms for component-by-component construction of rank-1 lattice rules in shift-invariant reproducing kernel Hilbert spaces
• Pricing Options Using Lattice Rules
• Component-By-Component Construction of Good Intermediate-Rank Lattice Rules
• Intermediate Rank Lattice Rules for Multidimensional Integration
• Lookback options with discrete and partial monitoring of the underlying price

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