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

17 Pages Posted: 25 Aug 2009 Last revised: 4 Jan 2016

See all articles by Poomjai Nacaskul, PhD, DIC, CFA

Poomjai Nacaskul, PhD, DIC, CFA

Siam Commercial Bank

Worawut Sabborriboon

Financial Institutions Strategy Department, Bank of Thailand

Date Written: August 24, 2009

Abstract

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.

Keywords: Copula, Gaussian Copula, 1-Factor Model, Goodness-of-Fit, US, Thai, Equity Data

JEL Classification: C02, C13, C14, G32

Suggested Citation

Nacaskul, Poomjai and Sabborriboon, Worawut, 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 (August 24, 2009). 22nd Australasian Finance and Banking Conference 2009. Available at SSRN: https://ssrn.com/abstract=1460576 or http://dx.doi.org/10.2139/ssrn.1460576

Poomjai Nacaskul (Contact Author)

Siam Commercial Bank ( email )

9 Ratchadaphisek Rd.
Chatuchak
Bangkok, Bangkok 10900
Thailand

HOME PAGE: http://www.scb.co.th

Worawut Sabborriboon

Financial Institutions Strategy Department, Bank of Thailand ( email )

273 Samsen Road
Bangkhunprom, Bangkok 10200
United States

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