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USV-Affine Models Without Derivatives: A Bayesian Time-Series Approach

Author

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  • Malefane Molibeli

    (School of Economics and Finance, University of the Witwatersrand, Johannesburg 2000, South Africa)

  • Gary van Vuuren

    (Centre for Business Mathematics and Informatics, North-West University, Potchefstroom Campus, Potchefstroom 2520, South Africa
    National Institute for Theoretical and Computational Sciences (NITheCS), Pretoria 0001, South Africa)

Abstract

We investigate the affine term structure models (ATSMs) with unspanned stochastic volatility (USV). Our aim is to test their ability to generate accurate cross-sectional behavior and time-series dynamics of bond yields. Comparing the restricted models and those with USV, we test whether they produce both reasonable estimates for the short rate variance and cross-sectional fit. Essentially, a joint approach from both time series and options data for estimating risk-neutral dynamics in ATSMs should be followed. Due to the scarcity of derivative data in emerging markets, we estimate the model using only time-series of bond yields. A Bayesian estimation approach combining Markov Chain Monte Carlo (MCMC) and the Kalman filter is employed to recover the model parameters and filter out latent state variables. We further incorporate macro-economic indicators and GARCH-based volatility as external validation of the filtered latent volatility process. The A 1 ( 4 ) USV performs better both in and out of sample, even though the issue of a tension between time series and cross-section remains unresolved. Our findings suggest that even without derivative instruments, it is possible to identify and interpret risk-neutral dynamics and volatility risk using observable time-series data.

Suggested Citation

  • Malefane Molibeli & Gary van Vuuren, 2025. "USV-Affine Models Without Derivatives: A Bayesian Time-Series Approach," JRFM, MDPI, vol. 18(7), pages 1-36, July.
  • Handle: RePEc:gam:jjrfmx:v:18:y:2025:i:7:p:395-:d:1703364
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