Applications of change of numéraire for option pricing
Date
2007-12
Authors
Le Roux, Gawie
Journal Title
Journal ISSN
Volume Title
Publisher
Stellenbosch : University of Stellenbosch
Abstract
The word numéraire refers to the unit of measurement used to value a portfolio of assets. The
change of numéraire technique involves converting from one measurement to another. The
foreign exchange markets are natural settings for interpreting this technique (but are by no means
the only examples).
This dissertation includes elementary facts about the change of numeraire technique. It also
discusses the mathematical soundness of the technique in the abstract setting of Delbaen and
Schachermayer’s Mathematics of Arbitrage. The technique is then applied to financial pricing
problems. The right choice of numéraire could be an elegant approach to solving a pricing problem
or could simplify computation and modelling.
Description
Thesis (MComm (Mathematics))--University of Stellenbosch, 2007.
Keywords
Numéraire, Dissertations -- Mathematics, Theses -- Mathematics, Options pricing, Arbitrage, Semi-martingales, Business mathematics, Financial instruments -- Prices, Options (Finance) -- Prices