Using Lattice Boltzmann Methods for Option Pricing

Summary

The note explores whether the lattice Boltzmann method, widely associated with computational fluid dynamics, could be applied to option pricing or other financial problems. The response points toward two relevant connections: lattice Boltzmann models for the Fokker–Planck equation and established partial differential equation methods for pricing under diffusion models. These references suggest a possible route from fluid and transport computation to probability-density evolution and derivative valuation.

The material is introductory rather than an implementation guide. It provides no algorithm, pricing formula, numerical comparison, or evidence that the method outperforms existing approaches. A reader interested in pursuing the idea would need to consult the referenced research and broader diffusion-based PDE pricing literature. The note’s useful contribution is therefore to identify conceptual and bibliographic starting points, while leaving questions of model setup, boundary conditions, accuracy, and computational performance unanswered.

Key ideas

• Lattice Boltzmann methods may connect to finance through models of the Fokker–Planck equation.
• Diffusion-based partial differential equation pricing methods offer a relevant framework for option valuation.
• The note points readers toward research references rather than explaining an implementation.
• It provides no comparison of numerical accuracy or performance against other pricing methods.

Tags

# Lattice Boltzmann method for pricing options


# Lattice Boltzmann method for pricing options












I'm looking into whether there is ANY information out there regarding the implementation of the Lattice Boltzmann method for pricing options (or other financial tasks). I am very new to the world of finance and it struck me that this might have a useful application (apart from fluid modelling).

Currently, I am a full-time MS student studying computational fluid dynamics while working part-time as a derivative structuring intern, and I figured it might be a nice future research topic.

Any info would be much appreciated.

## Answer by Quartz (score 1, accepted)

https://quant.stackexchange.com/a/10035

On one side there's a lot like A lattice Boltzmann model for the Fokker–Planck equation, on the other get a look at any PDE pricing method under diffusions. Also this is more directly on pricing.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.