On the Distribution of the Mixed-Lognormal-Weibull Option Pricing Model

Abstract

This paper intends to test whether the Mixed-Lognormal-Weibull Distribution (MLWD) option pricing model comes from the same distribution and whether the model is a good fit in Black-Scholes option pricing model. The data for this study were obtained from Australian Clearing House of Australian Securities Exchange (ASX) which consist of 50 enlisted stock as products of monthly market summary for long term options collected from January, 3rd 2017 to December, 31st 2017, comprising 720 trading days arranged in accordance to 25, 27, 28, 29 and 30 maturity days. Maximum Likelihood Estimate was used to obtain the parameters of both the lognormal and Weibull distributions which were applied in Black-Scholes model. The data were test Wilcoxon Rank Sum test since the mixture model became distribution and Chi-square goodness-of-fit test for the model fit, and the result shows that the mixture model does not follow any of the lognormal or Weibull distributions. The result also shows that the mixture model is a good fit in Black-Scholes option pricing model with the P-value>0.05 when they are shorter maturity days with small sample sizes than longer maturity days with larger sample sizes. Hence, the model is recommended to be used for financial practitioners who are interested in modeling option pricing.