Sensitivity estimation by Monte-Carlo simulation using likelihood ratio method with fixed-sample-path principle

The likelihood ratio method (LRM) is an efficient indirect method for estimating the sensitivity of given expectations with respect to parameters by Monte-Carlo simulation. The restriction on application of LRM to real-world problems is that it requires explicit knowledge of the probability density function (pdf) to calculate the score function. In this study, a fixed-sample-path method is proposed, which derives the score function required for LRM not via the pdf but directly from a constructive algorithm that computes the sample path from parameters and random numbers. The boundary residual, which represents the correction associated with the change of the distribution range of the random variables in LRM, is also derived. Some examples including the estimation of risk measures (Greeks) of option and financial flow-of-funds networks showed the effectiveness of the fixed-sample-path method.