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1 results

  • Efficient Estimation of One-Dimensional Diffusion First Passage Time Densities via Monte Carlo Simulation

  • Part of
  • Tomoyuki Ichiba, Constantinos Kardaras
  • Journal:
    Journal of Applied Probability / Volume 48 / Issue 3 / September 2011
    Published online by Cambridge University Press:
    14 July 2016, pp. 699-712
    Print publication:
    September 2011
    • Article
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  • We propose a method for estimating first passage time densities of one-dimensional diffusions via Monte Carlo simulation. Our approach involves a representation of the first passage time density as the expectation of a functional of the three-dimensional Brownian bridge. As the latter process can be simulated exactly, our method leads to almost unbiased estimators. Furthermore, since the density is estimated directly, a convergence of order 1 / √N, where N is the sample size, is achieved, which is in sharp contrast to the slower nonparametric rates achieved by kernel smoothing of cumulative distribution functions.