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Uncertain Parameters, an Empirical Stochastic Volatility Model and Confidence Limits

Author

Listed:
  • Paul Wilmott

    (Mathematical Institute, 24-29 St Giles', Oxford, OX1 3LB, UK;
    Department of Mathematics, Imperial College, Exhibition Road, SW7 2AZ London, UK)

  • Asli Oztukel

    (Mathematics Institute, 24-29 St Giles', Oxford, OX1 3LB, UK)

Abstract

In this paper we build upon the recently developed uncertain parameter framework for valuing derivatives in a worst-case scenario. We start by deriving a stochastic volatility model based on a simple analysis of time-series data. We use this stochastic model to examine the time evolution of volatility from an initial known value to a steady-state distribution in the long run. This empirical model is then incorporated into the uncertain parameter option valuation framework to provide "confidence limits" for the option value.

Suggested Citation

  • Paul Wilmott & Asli Oztukel, 1998. "Uncertain Parameters, an Empirical Stochastic Volatility Model and Confidence Limits," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 1(01), pages 175-189.
    • Handle: RePEc:wsi:ijtafx:v:01:y:1998:i:01:n:s0219024998000096
    DOI: 10.1142/S0219024998000096
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    Cited by:

    1. Tolulope Fadina & Ariel Neufeld & Thorsten Schmidt, 2018. "Affine processes under parameter uncertainty," Papers 1806.02912, arXiv.org, revised Mar 2019.
    2. Grajales Correa, Carlos Alexander & Pérez Ramírez, Fredy Ocaris & Venegas-Martínez, Francisco, 2014. "Análisis comparativo de modelos para estimar la distribución de la volatilidad de series financieras de rendimientos [A Comparative Analysis of Models for Estimating the Volatility Distribution of ," MPRA Paper 54845, University Library of Munich, Germany.
    3. Tak Kuen Siu, 2024. "Bayesian Lower and Upper Estimates for Ether Option Prices with Conditional Heteroscedasticity and Model Uncertainty," JRFM, MDPI, vol. 17(10), pages 1-32, September.
    4. Roberto Andreotti Bodra & Afonso De Campos Pint, 2014. "Modelo De Volatilidade Estocástica Com Saltos Aplicado A Commodities Agrícolas," Anais do XLI Encontro Nacional de Economia [Proceedings of the 41st Brazilian Economics Meeting] 142, ANPEC - Associação Nacional dos Centros de Pós-Graduação em Economia [Brazilian Association of Graduate Programs in Economics].
    5. Buchbinder, G.L. & Chistilin, K.M., 2007. "Multiple time scales and the empirical models for stochastic volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 379(1), pages 168-178.

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