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Volatility Estimation via Jump Indicator

Author

Listed:
  • R. Aboulaich
  • H. Ben Ameur
  • M. Lamarti Sefian

Abstract

The volatility is considered constant in Black and Scholes model. However, this implausible assumption leads to an undervaluation of options. We try to remediate to this drawback considering a more realistic model where the volatility is a piecewise constant function of time. We introduce a jump indicator to locate iteratively discontinuities of volatility and use an optimization process to estimate volatility values. We compare our results with regularization method (Aboulaich & Medarhri, 2013) and "AutoRegressive Conditional Heteroskedasticity" ARCH method (Engle, 1982).

Suggested Citation

  • R. Aboulaich & H. Ben Ameur & M. Lamarti Sefian, 2014. "Volatility Estimation via Jump Indicator," Modern Applied Science, Canadian Center of Science and Education, vol. 8(2), pages 1-12, April.
    • Handle: RePEc:ibn:masjnl:v:8:y:2014:i:2:p:12
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    References listed on IDEAS

    as
    1. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "An Intertemporal General Equilibrium Model of Asset Prices," Econometrica, Econometric Society, vol. 53(2), pages 363-384, March.
    2. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    3. Carl Chiarella & Mark Craddock & Nadima El-Hassan, 2000. "The Calibration of Stock Option Pricing Models Using Inverse Problem Methodology," Research Paper Series 39, Quantitative Finance Research Centre, University of Technology, Sydney.
    4. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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