2010/08/07 by Tomoyuki Ichiba, Ichiba, Tomoyuki, Constantinos Kardaras +1
Mathematics · Economics, Econometrics and Finance · #Stochastic processes and statistical mechanics #Stochastic processes and financial applications #Markov Chains and Monte Carlo Methods
paper · pdf · doi:10.48550/arxiv.1008.1326
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 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, the last being in sharp contrast to the slower non-parametric rates achieved by kernel smoothing of cumulative distribution functions.