Numeraire Invariance, Change of Measure, and Pricing by Arbitrage in Continuous Time Financial Models

The paper is in two major parts. In the setup of a standard continuous time model of a financial market with interest rate risk only, we first provide a comprehensible and intuitive exposition of the foundation for and relation between three valuation methodologies: the classical no arbitrage valuation method, the celebrated risk-neutral valuation method, and the lesser known forward-risk adjusted valuation technique. While the three techniques are equivalent from an economic perspective and therefore have identical implications for pricing, from a practitioners' perspective they each have their merits in different contexts. In particular, the forward-risk adjustment technique is appropriate when interest rate uncertainty prevails. We illustrate this with some new option pricing examples in the second part of the paper