Gaussian Slug - Simple Nonlinearity Enhancement to the 1-Factor and Gaussian Copula Models in Finance, with Parametric Estimation and Goodness-of-Fit Tests on US and Thai Equity Data

A bivariate normal distribution, with the attendant non-analytically integrable p.d.f., lies at the hearts of many financial theories. Its derived Gaussian copula ostensibly does away with the normality assumptions, only to retain the linear (Pearson's) correlation measure implicit to said bivariate normal p.d.f. In financial modelling context, the Gaussian copula suffer from at least three setbacks, namely its inability to capture (extreme) tail, asymmetric (upside vs. downside), and nonlinear (diminishing) dependency structures. Noting that various fixes have been proposed w.r.t. the former two issues, (i) this paper attempts to address the nonlinearity with the proposal of a bivariate ‘Gaussian Slug' distribution (ii) from which a derived copula density function quite naturally and parsimoniously captures a particular nonlinear dependency structure. In addition, (iii) this paper devises a simple, intuitive formulation of copula parameter estimation as a minimisation of a chi-square test statistics, (iv) whose resultant value readily lends itself to the widely popular statistical goodness-of-fit testing. Tests were performed comparing independent vs. Gaussian vs. ‘Gaussian Slug' copulas on weekly US and Thai equity market index and individual stock returns data, all available on Reuters