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AN EXPLICIT IMPLIED VOLATILITY FORMULA

Dan Stefanica () and Radoš Radoičić ()
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Dan Stefanica: Department of Mathematics, Baruch College, CUNY, One Bernard Baruch Way, New York, NY 10010, USA
Radoš Radoičić: Department of Mathematics, Baruch College, CUNY, One Bernard Baruch Way, New York, NY 10010, USA

International Journal of Theoretical and Applied Finance (IJTAF), 2017, vol. 20, issue 07, 1-32

Abstract: We show that an explicit approximate implied volatility formula can be obtained from a Black–Scholes formula approximation that is 2% accurate. The relative error of the approximate implied volatility is uniformly bounded for options with any moneyness and with arbitrary large or small option maturities and volatilities, including for long dated options and options on highly volatile underlying assets. For options within a large trading range, such as options with maturity less than five years and implied volatility less than 150%, the error of the approximate implied volatility relative to the Black–Scholes implied volatility is less than 10% points.

Keywords: Implied volatility; Black-Scholes model; approximation formula; uniform bounds (search for similar items in EconPapers)
Date: 2017
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