Estimation and Specification Test for Diffusion Models with Stochastic Volatility

TL;DR

This paper develops a goodness-of-fit test for stochastic volatility models in continuous time, using empirical processes and bootstrap calibration, with simulation and real data applications.

Contribution

It introduces a novel test for the parametric form of diffusion models with stochastic volatility, addressing discretely sampled data challenges.

Findings

Test performs well in simulation studies

Bootstrap method effectively calibrates the test

Application to real data demonstrates practical utility

Abstract

Given the importance of continuous-time stochastic volatility models to describe the dynamics of interest rates, we propose a goodness-of-fit test for the parametric form of the drift and diffusion functions, based on a marked empirical process of the residuals. The test statistics are constructed using a continuous functional (Kolmogorov-Smirnov and Cram\'er-von Mises) over the empirical processes. In order to evaluate the proposed tests, we implement a simulation study, where a bootstrap method is considered for the calibration of the tests. As the estimation of diffusion models with stochastic volatility based on discretely sampled data has proven difficult, we address this issue by means of a Monte Carlo study for different estimation procedures. Finally, an application of the procedures to real data is provided.