Generalized likelihood ratio method for stochastic models with uniform random numbers as inputs

Abstract

We propose a new unbiased stochastic gradient estimator for a family of stochastic models driven by uniform random numbers as inputs. Dropping the requirement that the tails of the density of the input random variables decay smoothly, the estimator extends the applicability of the generalized likelihood ratio (GLR) method. We demonstrate the new estimator for several general classes of input random variates, including independent inverse transform random variates and dependent input random variables governed by an Archimedean copula. We show how the new estimator works in settings such as density estimation, and we illustrate applications to credit risk derivatives. Numerical experiments substantiate broad applicability and flexibility in dealing with discontinuities in the sample performance.