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Modeling VIX Index Based on Semi-parametric Markov Models with Frank Copula/ VIX indeksa modelēšana, izmantojot neparametriskos Markova modeļus ar Franka kopulu/ Моделирование VIX индекса посредством непараметрических Марковских моделей с копулой Франка

Author

Listed:
  • Matvejevs Andrejs
  • Fjodorovs Jegors

    (Riga Technical University)

Abstract

Данная статья описывает алгоритм оценки непараметрической Марковской модели с помощью плотности копулы Франка. Копульные непараметрические регрессии отличаются тем, что исследователь может разделить различные виды (источники) риска, каждый смоделировать отдельно (непараметрические маргинальные распределения и параметрическая копульная функция) и соединить копулой, свободной от маштаба временной зависимостью. В статье был использован финансовый индекс VIX, измеряющий 30-дневную будущую внутреннюю волатильность на основе индекса акций S & P 500. Этот индекс рассчитывается, исходя из цен опционов. Описанный подход позволяет оценить параметры копулы Франка, правильность выбора которой устанавливается с помощью статистических критериев и является лучшим для данных индекса VIX. То есть эта копула лучше остальных копул описывает историческую зависимость. Далее, на основе функции плотности Франка копулы, был описан механизм оценки коэффициентов непараметрической Марковской регрессии. Такая оценка параметров трудоёмка - нет аналитического решения (параметрический интеграл расходится в точке 0). Таким образом, вычисление параметров происходит с использованием численных методов в пакетах Matlab и Mathematica. Проверить правильность подхода позволяют графические иллюстрации, где можно видеть, что второй момент, добавленный к уравнению, является нелинейным. В результате, используя описанную методологию, можно имитировать индекс VIX в разные промежутки времени и полученные результаты использовать в управлении финансовыми рисками (операции хеджирования через опционы) или принятии спекулятивных торговых позиций с опционами.

Suggested Citation

  • Matvejevs Andrejs & Fjodorovs Jegors, 2014. "Modeling VIX Index Based on Semi-parametric Markov Models with Frank Copula/ VIX indeksa modelēšana, izmantojot neparametriskos Markova modeļus ar Franka kopulu/ Моделирование VIX индекса посредством ," Information Technology and Management Science, Sciendo, vol. 17(1), pages 106-110, December.
  • Handle: RePEc:vrs:itmasc:v:17:y:2014:i:1:p:106-110:n:16
    DOI: 10.1515/itms-2014-0016
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    References listed on IDEAS

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    2. Stoll, Hans R. & Whaley, Robert E., 1990. "The Dynamics of Stock Index and Stock Index Futures Returns," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 25(4), pages 441-468, December.
    3. Ai[diaeresis]t-Sahalia, Yacine & Kimmel, Robert, 2007. "Maximum likelihood estimation of stochastic volatility models," Journal of Financial Economics, Elsevier, vol. 83(2), pages 413-452, February.
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