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Representation over Rents: Stochastic Volatility Models with Stable Disturbances: Estimation via Linearization

Author

Listed:
  • Fernando Roders

    (a.s.r. Asset Management)

  • Siem Jan Koopman

    (Vrije Universiteit Amsterdam)

  • Karim Moussa

    (Vrije Universiteit Amsterdam)

Abstract

In this study, we propose to estimate the parameters of stochastic volatility models with stable disturbances using methods based on linearization. Specifically, we obtain a linear state space form of the model by taking the logarithm of the squared financial returns, which, together with analytical expressions for logarithmic and fractional lower order moments of the stable distribution, forms the basis of the proposed quasi-maximum likelihood and generalized method of moments estimators. The methods are straightforward to implement and do not require simulation. We provide details of the implementation and study the finite-sample performance of the two estimation methods in a Monte Carlo study. The empirical relevance is illustrated by studying model-implied volatility estimates from time series of daily returns from stock indices, exchange rates, and cryptocurrencies.

Suggested Citation

  • Fernando Roders & Siem Jan Koopman & Karim Moussa, 2026. "Representation over Rents: Stochastic Volatility Models with Stable Disturbances: Estimation via Linearization," Tinbergen Institute Discussion Papers 26-082/II, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20260082
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    More about this item

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G15 - Financial Economics - - General Financial Markets - - - International Financial Markets

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