Generalized Likelihood Ratio Method for Stochastic Models with Uniform Random Numbers As Inputs

We propose a new unbiased stochastic gradient estimator for a family of stochastic models with uniform random numbers as inputs. By extending the generalized likelihood ratio (GLR) method, the proposed estimator applies to discontinuous sample performances with structural parameters without requiring that the tails of the density of the input random variables go down to zero smoothly, an assumption in Peng et al. (2018) and Peng et al. (2020a) that precludes a direct formulation in terms of uniform random numbers as inputs. By overcoming this limitation, our new estimator greatly expands the applicability of the GLR method, which we demonstrate for several general classes of uniform input random numbers, including independent inverse transform random variates and dependent input random variables governed by an Archimedean copula. We show how the new derivative estimator works in specific settings such as density estimation, distribution sensitivity for quantiles, and sensitivity analysis for Markov chain stopping time problems, which we illustrate with applications to statistical quality control, stochastic activity networks, and credit risk derivatives. Numerical experiments substantiate broad applicability and flexibility in dealing with discontinuities in sample performance

Monte Carlo Greeks for financial products via approximative transition densities

In this paper we introduce efficient Monte Carlo estimators for the valuation of high-dimensional derivatives and their sensitivities (''Greeks''). These estimators are based on an analytical, usually approximative representation of the underlying density. We study approximative densities obtained by the WKB method. The results are applied in the context of a Libor market model.Comment: 24 page

A Generalisation of Malliavin Weighted Scheme for Fast Computation of the Greeks

This paper presented a new technique for the simulation of the Greeks (i.e. price sensitivities to parameters), efficient for strongly discontinuous payo¤ options. The use of Malliavin calculus, by means of an integration by parts, enables to shift the differentiation operator from the payo¤ function to the diffusion kernel, introducing a weighting function.(Fournie et al. (1999)). Expressing the weighting function as a Skorohod integral, we show how to characterize the integrand with necessary and sufficient conditions, giving a complete description of weighting function solutions. Interestingly, for adapted process, the Skorohod integral turns to be the classical Ito integral.Monte-Carlo, Quasi-Monte Carlo, Greeks,Malliavin Calculus, Wiener Chaos.

Random number generation with multiple streams for sequential and parallel computing

International audienceWe provide a review of the state of the art on the design and implementation of random number generators (RNGs) for simulation, on both sequential and parallel computing environments. We focus on the need for multiple streams and substreams of random numbers, explain how they can be constructed and managed, review software libraries that offer them, and illustrate their usefulness via examples. We also review the basic quality criteria for good random number generators and their theoretical and empirical testing