Bounds on baskets option prices

The celebrated Black-Scholes option pricing model is unable to produce closed-form solutions for arithmetic basket options. This problem stems from the lack of an analitical form for the distribution of a sum of lognormal random variables. lVlarket participants commonly price basket options by assuming the basket follows lognormal dynamics, although it is known that this approximation performs poorly in some cicumstances. The problem of finding an analytical approximation to the sum of lognormally distributed random variables has been widely studied. In this dissertation we seek to draw these studies together and apply them in an option pricing setting. We propose some new option pricing formulae based on these approximations. In order to examine the utility of these new formulae and compare them to commonly used market approximations we present rigorous analytical bounds for the price of arithmetic basket options using the theory of comonotonicity. In this we follow the ideas in Deelstra et al. [7]. Additionally we provide an interval of hedge parameters (the Greeks). We carry out a numerical sensitivity analysis and identify circumstances under which the market approximation misprices basket options.

Grantor dc:publisher.institution

Department of Mathematics and Applied Mathematics

Year dc:date.issued

2005

Author dc:creator

• De Swardt, N C

Advisor dc:contributor.advisor

• Polakow, Daniel

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/11427/4880

OAI identifier oai:identifier

oai:open.uct.ac.za:11427/4880