Alternative Measures to Test the Stability of Implied Probability Density Functions

Abstract

To assess the stability of probability density functions (PDFs) implied by option prices, we develop and apply alternative measures other than distributional characteristics. Our alternative measures are related to the stability of empirical results in the applications of implied PDFs such as pricing thinly traded options and recovering the risk aversion of investors. Using the KOSPI 200 index options in the Korean market, we compare the performance between the double lognormal approximating function (DLN) method and the smoothed implied volatility smile (SMIV) method which are most widely used for estimating implied PDFs. Our empirical results show that while the SMIV method can produce a PDF with more stable summary statistics as in most previous researches, it cannot outperform the DLN method in terms of other measures. The sensitivity analysis by using the randomly perturbed prices increases the validity of our findings.