# Likelihood Evaluation of Jump-Diffusion Models Using Deterministic Nonlinear Filters

## TL;DR

This paper introduces a deterministic nonlinear filtering approach to efficiently evaluate likelihood functions for jump-diffusion models with stochastic volatility and jumps, outperforming particle filters in speed and smoothness.

## Contribution

The authors develop a high-dimensional deterministic filtering algorithm for complex jump-diffusion models, providing a faster and more precise alternative to particle filters.

## Key findings

- Deterministic filtering is more accurate and faster than particle filtering.
- Maximum likelihood estimates reveal increased jump intensity during the Great Recession.
- Jump components significantly contribute to volatility clustering and negative returns.

## Abstract

In this study, we develop a deterministic nonlinear filtering algorithm based on a high-dimensional version of Kitagawa (1987) to evaluate the likelihood function of models that allow for stochastic volatility and jumps whose arrival intensity is also stochastic. We show numerically that the deterministic filtering method is precise and much faster than the particle filter, in addition to yielding a smooth function over the parameter space. We then find the maximum likelihood estimates of various models that include stochastic volatility, jumps in the returns and variance, and also stochastic jump arrival intensity with the S&P 500 daily returns. During the Great Recession, the jump arrival intensity increases significantly and contributes to the clustering of volatility and negative returns.