Volatility Estimation via Jump Indicator

R. Aboulaich, H. Ben Ameur, M. Lamarti Sefian


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).

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DOI: https://doi.org/10.5539/mas.v8n2p12

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