Pricing 2-colour rainbows : nonparametric methods using copulae

This paper investigates the use of copulae for non parametric pricing of multivariate contingent claims. Price estimates and no-arbitrage bounds for various types of two-colour rainbow options on the South African equity and bond markets were calculated. Implied marginal risk-neutral distributions were derived nonparametrically from each assets option price spread. This was achieved in a very simple manner by assuming that, for each of the underlying assets in question, a continuum of option prices exist. Cubic splines were used to fit this continuum to the implied volatilities of the actual options available. Two nonparametric copulae were considered: an empirical copula based directly upon the data and a kernel copula derived from a smooth two-dimensional kernel approximation of the historic density function. In addition, various parametric copulae were considered for comparison purposes. The differences between each of these approaches was found to vary from one type of rainbow to another.

Grantor dc:publisher.institution

School of Economics

Year dc:date.issued

2005

Author dc:creator

• Knox, Sean D

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/11427/11778

OAI identifier oai:identifier

oai:open.uct.ac.za:11427/11778