On the Use of Numeraires in Option Pricing

Abstract

Significant computational simplification is achieved when option pricing is approached through the change of numeraire technique. By pricing an asset in terms of another traded asset (the numeraire), this technique reduces the number of sources of risk that need to be accounted for. The technique is useful in pricing complicated derivatives.

This article discusses the underlying theory of the numeraire technique, and illustrates it with five pricing problems: pricing savings plans that offer a choice of interest rates; pricing convertible bonds; pricing employee stock ownership plans; pricing options whose strike price is in a currency different from the stock price; and pricing options whose strike price is correlated with the short-term interest rate.

Keywords: options, numeraire

JEL Classification: G12, G13