TIGHTER BOUNDS FOR IMPLIED VOLATILITY

Jim Gatheral (), Ivan Matić (), Radoš Radoičić () and Dan Stefanica ()
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Jim Gatheral: Department of Mathematics, Baruch College, City University of New York, One Bernard Baruch Way, New York 10010, USA
Ivan Matić: Department of Mathematics, Baruch College, City University of New York, One Bernard Baruch Way, New York 10010, USA
Radoš Radoičić: Department of Mathematics, Baruch College, City University of New York, One Bernard Baruch Way, New York 10010, USA
Dan Stefanica: Department of Mathematics, Baruch College, City University of New York, One Bernard Baruch Way, New York 10010, USA

International Journal of Theoretical and Applied Finance (IJTAF), 2017, vol. 20, issue 05, 1-14

Abstract: We establish bounds on Black–Scholes implied volatility that improve on the uniform bounds previously derived by Tehranchi. Our upper bound is uniform, while the lower bound holds for most options likely to be encountered in practical applications. We further demonstrate the practical effectiveness of our new bounds by showing how the efficiency of the bisection algorithm is improved for a snapshot of SPX option quotes.

Keywords: Implied volatility; Pólya approximation; bisection method (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (4)

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DOI: 10.1142/S0219024917500352

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