# Multilevel Monte Carlo Method for Path-Dependent Barrier Interest Rate Derivatives

Building on the LIBOR market models, this paper considers some   path-dependent barrier interest rate derivatives whose barrier events are monitored at a set of reset dates. A multilevel Monte Carlo method is developed to compute their prices. With incorporation of the conditioning on one-step survival technique, the multilevel estimator is carefully constructed such that the computational cost for the resulting multilevel algorithm to achieve an $\epsilon$ root-mean-square-error is $O(\epsilon^{-2}).$

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