Comparison of low discrepancy mesh methods for pricing Bermudan options under a Lévy process

Research output: Contribution to journalArticle

Abstract

This paper discusses simulation methods for pricing Bermudan options under an exponential Lévy process. We investigate an efficient simulation approach that can generate sample trajectories from an explicitly known density function under an exponential Lévy process. The paper examines the impact of the choice of mesh density for sampling trajectories on the efficiency of both the low discrepancy and stochastic mesh methods. Three mesh densities are introduced and compared, that is, average, marginal and squared average. Numerical experiments show that the squared average density is the best choice for the mesh density function in pricing Bermudan put options under an exponential normal inverse Gaussian Lévy process. The low discrepancy mesh method using the squared average density can provide unbiased estimates with a smaller number of mesh points. Furthermore, it can provide estimates with the smallest standard error.

Original languageEnglish
Pages (from-to)54-71
Number of pages18
JournalMathematics and Computers in Simulation
Volume100
DOIs
Publication statusPublished - 2014

Fingerprint

Option Pricing
Probability density function
Discrepancy
Trajectories
Mesh
Costs
Sampling
Density Function
Trajectory
Inverse Gaussian
Experiments
Standard error
Gaussian Process
Simulation Methods
Estimate
Pricing
Numerical Experiment
Simulation

Keywords

  • Bermudan option
  • Lévy process
  • Low discrepancy mesh method
  • Quasi-Monte Carlo

ASJC Scopus subject areas

  • Modelling and Simulation
  • Numerical Analysis
  • Applied Mathematics
  • Theoretical Computer Science
  • Computer Science(all)

Cite this

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title = "Comparison of low discrepancy mesh methods for pricing Bermudan options under a L{\'e}vy process",
abstract = "This paper discusses simulation methods for pricing Bermudan options under an exponential L{\'e}vy process. We investigate an efficient simulation approach that can generate sample trajectories from an explicitly known density function under an exponential L{\'e}vy process. The paper examines the impact of the choice of mesh density for sampling trajectories on the efficiency of both the low discrepancy and stochastic mesh methods. Three mesh densities are introduced and compared, that is, average, marginal and squared average. Numerical experiments show that the squared average density is the best choice for the mesh density function in pricing Bermudan put options under an exponential normal inverse Gaussian L{\'e}vy process. The low discrepancy mesh method using the squared average density can provide unbiased estimates with a smaller number of mesh points. Furthermore, it can provide estimates with the smallest standard error.",
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AB - This paper discusses simulation methods for pricing Bermudan options under an exponential Lévy process. We investigate an efficient simulation approach that can generate sample trajectories from an explicitly known density function under an exponential Lévy process. The paper examines the impact of the choice of mesh density for sampling trajectories on the efficiency of both the low discrepancy and stochastic mesh methods. Three mesh densities are introduced and compared, that is, average, marginal and squared average. Numerical experiments show that the squared average density is the best choice for the mesh density function in pricing Bermudan put options under an exponential normal inverse Gaussian Lévy process. The low discrepancy mesh method using the squared average density can provide unbiased estimates with a smaller number of mesh points. Furthermore, it can provide estimates with the smallest standard error.

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