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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.

Frontmatter -- Contents -- Acknowledgments -- 1. Making Education Policy Here, There, and Everywhere -- 2. Doing Standards: Content and Context -- 3. Interactive Policymaking -- 4. Making Policy, Making Sense -- 5. Resources for Sense-Making -- 6. The Schoolteacher and Interactive Policymaking -- 7. Policy in Practice -- 8. Implementation Reconsidered -- Appendix: Research Methods -- References -- Index

A least squares solution for the scale values obtained by using the method of successive intervals for the basic observational data is derived. The theoretical solution depends upon solving simultaneously for the scale values (mi), the discriminal dispersions (si), and the category boundaries (tg) which will minimize the quantity (formula not translated) where zig is a normal deviate corresponding to an observed % and b is an arbitrarily assigned standard deviation for tg. Numerically the direct least squares solution is laborious. Methods for simplifying the computations are presented. A series of numerical examples compare the relative accuracy of scales obtained from various occupational procedures. B. J. Winer (AJASA).

AbstractHere, the relationship between Value Line rankings and option implied standard deviations is investigated. Each Value Line ranking (safety, price stability, timeliness, and earnings predictability) is significantly related to option implied standard deviations for a sample of 62 companies with Value Line timeliness rankings of 1, 2, 4, and 5 and with a total of 1,217 call options traded over a 3‐day period. The index for price stability would be most valuable to investors for assessing future risk since only this index has a significant association with residual implied volatility, i.e., those unexplained by historical volatility.

A survey revealed that researchers still seem to encounter difficulties to cope with outliers. Detecting outliers by determining an interval spanning over the mean plus/minus three standard deviations remains a common practice. However, since both the mean and the standard deviation are particularly sensitive to outliers, this method is problematic. We highlight the disadvantages of this method and present the median absolute deviation, an alternative and more robust measure of dispersion that is easy to implement. We also explain the procedures for calculating this indicator in SPSS and R software. ; info:eu-repo/semantics/published