A Comparison of Formulas to Compute Implied Standard Deviation

James S. Ang (), Gwoduan David Jou () and Tsong-Yue Lai ()
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James S. Ang: College of Business, Florida State University
Gwoduan David Jou: CFO, Taikang Life Insurance Co.
Tsong-Yue Lai: California State University, Fullerton

Chapter 65 in Encyclopedia of Finance, 2022, pp 1511-1529 from Springer

Abstract: Abstract We derive an exact closed-form solution for the implied standard deviation in the Black and Scholes’ option pricing model under the condition that the underlying asset price equals the present value of the exercise price. The exact closed-form solution provides the true implied standard deviation and has no estimation error. We then relax this condition and develop three new formulas that depend on a Taylor series expansion utilizing one, two or three options. Simulations show these formulas produce lower estimation errors than extant approaches, and the third formula gives the best overall results under different parameter values.

Keywords: Implied standard deviation; Implied volatility; Options; Option pricing model; Taylor formula (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/978-3-030-91231-4_65

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