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Pólya-based approximation for the ATM-forward implied volatility

Ivan Matić (ivan.matic@baruch.cuny.edu), Radoš Radoičić (rados.radoicic@baruch.cuny.edu) and Dan Stefanica (dan.stefanica@baruch.cuny.edu)
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Ivan Matić: Department of Mathematics, Baruch College, CUNY, One Bernard Baruch Way, New York 10010, USA
Radoš Radoičić: Department of Mathematics, Baruch College, CUNY, One Bernard Baruch Way, New York 10010, USA
Dan Stefanica: Department of Mathematics, Baruch College, CUNY, One Bernard Baruch Way, New York 10010, USA

International Journal of Financial Engineering (IJFE), 2017, vol. 04, issue 02n03, 1-15

Abstract: We introduce a closed form approximation for the implied volatility of ATM-forward options. The relative error of this approximation is uniformly bounded for all option maturities and implied volatilities. The approximation is extremely precise, having relative error less than 10−6 for all options with integrated volatility less than 1.9, such as options with maturity less than three years and implied volatility less than 100%. Moreover, the approximate implied volatilities fall within the implied volatility bid–ask spread for all the liquid options, such as options with volatility less than 200% and maturity less than nine years.

Keywords: Implied volatility; Pólya-based approximation; ATM options (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (3)

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DOI: 10.1142/S2424786317500323

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