A0377
Title: Using regression to enhance an existing closed-form implied volatility formula to widen the range of option moneyness
Authors: Wei-Chung Miao - National Taiwan University of Science and Technology (Taiwan) [presenting]
Abstract: In the option pricing literature, there are a number of closed-form formulas for implied volatility that allow for the fast construction of the implied volatility surface. Among others, perhaps the best-performing formula is the version of an existing study developed based on rational approximation. While the formula works nicely for options that are near-the-money, its accuracy deteriorates as the moneyness deviates from 0 (standing for at-the-money), and this greatly limits its applicability. The intention is to develop a closed-form formula that can be applied to options with moneyness away from 0. With this formula accompanied, the original formula can be significantly enhanced and becomes applicable for options with much-widened moneyness. The approach is based on a regression of implied volatility on its explanatory variables. Through the identification of key variables as well as the establishment of the proper functional form, the regression-based closed-form formula is successfully developed with high R-squared and is shown to provide nice accuracy. The numerical results show that when the original formula is enhanced by the regression-based formula, the implied volatility can be accurately calculated with absolute percentage error reduced to lower than 1\% for options with moneyness over a wide range.
