Multilevel particle filters for Lévy-driven stochastic differential equations

Ajay Jasra, Kody J.H. Law, Prince Peprah Osei

    Research output: Contribution to journalArticlepeer-review


    We develop algorithms for computing expectations with respect to the laws of models associated to stochastic differential equations driven by pure Lévy processes. We consider filtering such processes as well as pricing of path dependent options. We propose a multilevel particle filter to address the computational issues involved in solving these continuum problems. We show via numerical simulations and theoretical results that under suitable assumptions regarding the discretization of the underlying driving Lévy proccess, the cost to obtain MSE O(ϵ2) scales like O(ϵ- 2) for our method, as compared with the standard particle filter O(ϵ- 3).

    Original languageEnglish
    JournalStatistics and Computing
    Early online date20 Oct 2018
    Publication statusPublished - 2018


    • Barrier options
    • Lévy processes
    • Lévy-driven SDE
    • Multilevel particle filters
    • Particle filters


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