Residual-Bridge Constructs for Conditioned Diffusions

TL;DR

This paper proposes a novel residual-bridge method for simulating conditioned diffusions, improving efficiency especially with variable volatilities and larger time gaps, by extending existing residual-bridge constructs.

Contribution

It introduces a new residual-bridge proposal that accounts for non-constant volatilities, enhancing simulation efficiency over previous methods.

Findings

Demonstrates improved efficiency in simulations with variable volatilities.

Shows gains over existing residual-bridge methods for larger inter-observation times.

Validates the approach through simulation studies.

Abstract

We introduce a new residual-bridge proposal for approximately simulating conditioned diffusions. This proposal is formed by applying the modified diffusion bridge approximation of Durham and Gallant (2002) to the difference between the true diffusion and a second, approximate diffusion driven by the same Brownian motion, and can be viewed as a natural extension to recent work on residual-bridge constructs (Whitaker et al., 2016). This new proposal attempts to account for volatilities which are not constant and can therefore lead to gains in efficiency over the recently proposed residual-bridge constructs in situations where the volatility varies considerably, as is often the case for larger inter-observation times and for time-inhomogeneous volatilities. These potential gains in efficiencies are illustrated via a simulation study.