ABSTRACT
Binomial models for the price evolution assume that the price of an asset X in terms of a reference asset Y in the next time instant will take only two possible values – an uptick or a downtick. These models are typically too simple to capture market reality. The main reason to include them in this book is to illustrate the fundamental concepts of derivative pricing in a simple model. We will later extend our analysis to more complex models, in particular to diffusions, and to models with jumps. In this chapter we show how to apply the First Fundamental Theorem of Asset Pricing on contracts written on two assets X and Y . Both assets X and Y can be used as reference assets for pricing European option contracts. We show how the pricing martingale measures that come with the assets X and Y are related, using both the basic martingale principles, and their relationship through the Radon-Nikody´m derivative. The approach of using both reference assetsX and Y is novel; most of the current literature uses only one reference asset, typically represented by a money market account, to price derivative contracts. In particular, we give two alternative characterizations of the price of a contingent claim using both reference assets.
