Semiparametric stochastic volatility modelling using penalized splines

TL;DR

This paper introduces a flexible nonparametric method for estimating the distribution in stochastic volatility models using penalized splines, avoiding strict distributional assumptions and enhancing modeling adaptability.

Contribution

It presents a novel maximum penalized likelihood approach combining hidden Markov models and penalized B-splines for semiparametric SV modeling, offering an alternative to Bayesian methods.

Findings

Feasibility demonstrated through simulation studies.

Applied to stock and index return data with promising results.

Provides a flexible framework for nonparametric distribution estimation.

Abstract

Stochastic volatility (SV) models mimic many of the stylized facts attributed to time series of asset returns, while maintaining conceptual simplicity. The commonly made assumption of conditionally normally distributed or Student-t-distributed returns, given the volatility, has however been questioned. In this manuscript, we introduce a novel maximum penalized likelihood approach for estimating the conditional distribution in an SV model in a nonparametric way, thus avoiding any potentially critical assumptions on the shape. The considered framework exploits the strengths both of the powerful hidden Markov model machinery and of penalized B-splines, and constitutes a powerful and flexible alternative to recently developed Bayesian approaches to semiparametric SV modelling. We demonstrate the feasibility of the approach in a simulation study before outlining its potential in applications to three series of returns on stocks and one series of stock index returns.