Applications of change of numéraire for option pricing

Le Roux, Gawie (2007-12)

Thesis (MComm (Mathematics))--University of Stellenbosch, 2007.


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.

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