On the Use of Numeraires in Option Pricing

Abstract

In this paper we discuss the significant computational simplification that occurs when option pricing is approached through the change of numeraire technique. The original impetus was a recently published paper on endowment options (Hoang, Powell, Shi 1999). We show that the HPS analysis can be simplified and extended by the use of numeraire techniques. We extend these results to the case of stochastic interest rates. We also discuss four additional option pricing problems within the framework of a change of numeraire:

- Pricing savings plans which incorporate a choice of linkage.

- Pricing convertible bonds.

- Pricing employee stock ownership plans

- Pricing options where the strike price is in a currency different from the stock price.

Keywords: Options, Numeraire, Convertible Bonds, Employee Stock Options, Currency Options

JEL Classification: G12