We seek a closed-form series approximation of European option prices under a variety of
diffusion models. The proposed convergent series are derived using the Hermite polynomial …

In this paper, we provide a unified approach to simulate diffusion bridges. The proposed
method covers a wide range of processes including univariate and multivariate diffusions …

A novel method is presented for estimating the parameters of a parametric diffusion process.
The approach is based on a closed-form Maximum Likelihood estimator for an …

The R package calculus implements C++-optimized functions for numerical and symbolic
calculus, such as the Einstein summing convention, fast computation of the LeviCivita …

In this paper we develop a new delta expansion approach to deriving analytical
approximation to the transition densities of multivariate diffusions using the Itô-Taylor …

“Supplementary Material”(Iguchi, Beskos and Graham, 2025) provides the proofs of the main
results and related technical proofs, and also contains an additional numerical experiment of …

A continuous-time diffusion process is very popular in modeling and provides useful tools to
analyze particularly, but not restricted to, a variety of economic and financial variables. The …

Assuming that a threshold Ornstein–Uhlenbeck process is observed at discrete time
instants, we propose generalized moment estimators to estimate the parameters. Our …

This paper is concerned with the parameter estimation problem for Cox–Ingersoll–Ross
model based on discrete observation. First, a new discretized process is built based on the …

The indispensable role of likelihood expansions in financial econometrics for continuous-
time models has been established since the ground-breaking work of Aït-Sahalia (1999 …