Stochastic volatility (SV) models mimic many of the stylized facts attributed to time series of asset returns, while maintaining conceptual simplicity. A substantial body of research deals with various techniques for fitting relatively basic SV models, which assume the returns to be conditionally normally distributed or Student-t-distributed  , given the volatility  . In this manuscript, we consider a frequentist framework for estimating the conditional distribution in an SV model in a nonparametric way, thus avoiding any potentially critical assumptions on the shape . More specifically, we suggest to represent the density of the conditional distribution as a linear combination of standardized B-spline basis functions, imposing a penalty term in order to arrive at a good balance between goodness of fit and smoothness. This allows us to employ the efficient hidden Markov model machinery in order to fit the model and to assess its predictive performance. We demonstrate the feasibility of the approach in a simulation study before applying it to three series of returns on stocks and one series of stock index returns. The nonparametric approach leads to an improved predictive capacity in some cases, and we find evidence for the conditional distributions being leptokurtic and negatively skewed .
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 discuss a penalized maximum likelihood approach for estimating the conditional distribution in an SV model in a nonparametric way, thus avoiding any potentially critical assumptions on the shape .
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A substantial body of research deals with various techniques for fitting relatively basic SV models, which assume the returns to be
The commonly made assumption of
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returns
A
, has however been questioned
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consider a frequentist framework
discuss a penalized maximum likelihood approach
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. More specifically, we suggest to represent the density of the conditional distribution as a linear combination of standardized B-spline basis functions, imposing a penalty term in order to arrive at a good balance between goodness of fit and smoothness. This allows us to employ the efficient hidden Markov model machinery in order to fit the model and to assess its predictive performance. We demonstrate the feasibility of the approach in a simulation study before applying it to three series of returns on stocks and one series of stock index returns. The nonparametric approach leads to an improved predictive capacity in some cases, and we find evidence for the conditional distributions being leptokurtic and negatively skewed