# Semiparametric stochastic volatility modelling using penalized splines

## 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 hidden Markov model machinery and of penalized B-splines, and constitutes a powerful 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.

## Keywords

B-splines Cross-validation Forward algorithm Hidden Markov model Numerical integration Penalized likelihood## Notes

### Acknowledgments

The authors would like to thank the two anonymous referees who provided useful comments on an earlier version of this manuscript.

## Supplementary material

## References

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