Robust the implied volatility linear function for ad hoc Black Scholes approaches | Abstract
Journal of Stock & Forex Trading

Journal of Stock & Forex Trading
Open Access

ISSN: 2168-9458



Robust the implied volatility linear function for ad hoc Black Scholes approaches

Muhammad Atif Sattar*, Felix E Arcilla

There are two ad hoc approaches (absolute smile and relative smile) to the Black Scholes model. We study a number of issues related to the ad hoc Black Scholes model. The Logarithmic transformation is applied to the implied volatility in the linear regression to ensure that the forecast is positive. Simply, retransformations from log to original matric to fitted values that are plugged into Black Scholes yield biased results because the Black Scholes formula is a non-linear function of implied volatility. In order to overcome this bias [1]smearing technique has been applied in this study. The Smearing estimation method also provides a biased yield if there is heteroscedasticity in OLS estimation residuals. We apply the weighted least square regression in order to avoid heteroscedasticity. Mean bias (MB), Mean absolute error (MAE), and Mean absolute relative error (MARE) are performance measures that concluded the smearing method is the finest to correct the bias in ad hoc Black Scholes approaches. Absolute smile is better than a relative smile without smearing technique but with smearing methods results are vice versa. Keywords: Option valuation; ad hoc Black Scholes; Absolute smile approach; Relative smile approach; Smearing technique; weighted regression; Heteroscedasticity.

Published Date: 2021-03-25; Received Date: 2021-03-05