Hybrid simulation scheme for volatility modulated moving average fields

TL;DR

This paper introduces a hybrid simulation scheme for volatility modulated moving average fields that accurately captures local roughness and global dependence, improving simulation performance for spatial stochastic processes.

Contribution

It develops a novel hybrid simulation method that approximates the kernel locally by a power function and elsewhere by a step function, with proven asymptotic mean square error.

Findings

The scheme effectively captures local roughness and long-range dependence.

It outperforms other simulation techniques in accuracy and efficiency.

The asymptotic mean square error is derived and validated.

Abstract

We develop a simulation scheme for a class of spatial stochastic processes called volatility modulated moving averages. A characteristic feature of this model is that the behaviour of the moving average kernel at zero governs the roughness of realisations, whereas its behaviour away from zero determines the global properties of the process, such as long range dependence. Our simulation scheme takes this into account and approximates the moving average kernel by a power function around zero and by a step function elsewhere. For this type of approach the authors of [8], who considered an analogous model in one dimension, coined the expression hybrid simulation scheme. We derive the asymptotic mean square error of the simulation scheme and compare it in a simulation study with several other simulation techniques and exemplify its favourable performance in a simulation study.