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How many inner simulations to compute conditional expectations with least-square Monte Carlo?

Author

Listed:
  • Aur'elien Alfonsi

    (MATHRISK, CERMICS)

  • Bernard Lapeyre

    (MATHRISK, CERMICS)

  • J'er^ome Lelong

    (DAO)

Abstract

The problem of computing the conditional expectation E[f (Y)|X] with least-square Monte-Carlo is of general importance and has been widely studied. To solve this problem, it is usually assumed that one has as many samples of Y as of X. However, when samples are generated by computer simulation and the conditional law of Y given X can be simulated, it may be relevant to sample K $\in$ N values of Y for each sample of X. The present work determines the optimal value of K for a given computational budget, as well as a way to estimate it. The main take away message is that the computational gain can be all the more important that the computational cost of sampling Y given X is small with respect to the computational cost of sampling X. Numerical illustrations on the optimal choice of K and on the computational gain are given on different examples including one inspired by risk management.

Suggested Citation

  • Aur'elien Alfonsi & Bernard Lapeyre & J'er^ome Lelong, 2022. "How many inner simulations to compute conditional expectations with least-square Monte Carlo?," Papers 2209.04153, arXiv.org, revised May 2023.
    • Handle: RePEc:arx:papers:2209.04153
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