Alternative Formulas to Compute Implied Standard Deviation

James S. Ang (), Gwoduan David Jou () and Tsong-Yue Lai ()
Additional contact information
James S. Ang: Department of Finance, Florida State University, Tallahassee, FL 32306–1042, USA
Gwoduan David Jou: Department of Finance, National Taiwan University, Taipei, Taiwan
Tsong-Yue Lai: Department of Finance, California State University-Fullerton, Fullerton, CA 92634, USA

Review of Pacific Basin Financial Markets and Policies (RPBFMP), 2009, vol. 12, issue 02, 159-176

Abstract: We assume that the call option's value is correctly priced by Black and Scholes' option pricing model in this paper. This paper derives an exact closed-form solution for implied standard deviation 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 estimate error. This paper also develops three alternative formulas to estimate the implied standard deviation if this condition is violated. Application of the Taylor expansion on a single call option value derives the first formula. The accuracy of this formula depends on the deviation between the underlying asset price and the present value of the exercise price. Use of the Taylor formula on two call option prices with different exercise prices is used to develop the second formula, which can be used even though the underlying asset price deviates significantly from the present value of the exercise price. Extension of the second formula's approach to third options value derives the third formula. A merit of the third formula is to circumvent a required parameter used in the second formula. Simulations demonstrate that the implied standard deviations calculated by the second and third formulas provide accurate estimates of the true implied standard deviations.

Keywords: Implied volatility; options; option pricing model; implied standard deviation; Taylor formula (search for similar items in EconPapers)
JEL-codes: G1 G2 G3 (search for similar items in EconPapers)
Date: 2009
References: View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S0219091509001599
Access to full text is restricted to subscribers

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:rpbfmp:v:12:y:2009:i:02:n:s0219091509001599

Ordering information: This journal article can be ordered from

DOI: 10.1142/S0219091509001599

Access Statistics for this article

Review of Pacific Basin Financial Markets and Policies (RPBFMP) is currently edited by Cheng-few Lee

More articles in Review of Pacific Basin Financial Markets and Policies (RPBFMP) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().