Estimation of parametric and nonparametric models for univariate loss distributions in finance—an approach using R

This paper presents an analysis of daily percentage stock returns from two companies listed on the Australian stock exchange. We estimate the probability density function of these returns using parametric and non-parametric methods. The methods are implemented using R. Parametric analysis includes estimation of normal and lognormal distributions for the two return series. Nonparametric analysis presented involves kernel density estimation. We illustrate the benefits of applying transformations to data prior to employing kernel based methods. We use a log-transformation and an optimal transformation amongst a class of transformations that produces symmetry in the data. The aim is to provide educators with material that can be used in the classroom to teach statistical estimation methods, goodness of fit analysis and importantly statistical computing in the context of finance, insurance and risk management. An appendix with further mathematical detail and R code is available from the first author.