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A Comparison of Formulas to Compute Implied Standard Deviation

In: Encyclopedia of Finance

Author

Listed:
  • James S. Ang

    (College of Business, Florida State University)

  • Gwoduan David Jou

    (CFO, Taikang Life Insurance Co.)

  • Tsong-Yue Lai

    (California State University, Fullerton)

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.

Suggested Citation

  • James S. Ang & Gwoduan David Jou & Tsong-Yue Lai, 2022. "A Comparison of Formulas to Compute Implied Standard Deviation," Springer Books, in: Cheng-Few Lee & Alice C. Lee (ed.), Encyclopedia of Finance, edition 0, chapter 65, pages 1511-1529, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-91231-4_65
    DOI: 10.1007/978-3-030-91231-4_65
    as

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