An Introduction to Exotic Option Pricing

Chapter 6

Two-Asset Rainbow Options

In this chapter we introduce the reader to a special class of multi-asset or rainbow options. Dual-asset options have an expiry T payoff of the form V (x, y, T) = f (x, y), where x and y denote prices of two distinct assets X and Y, which are generally correlated. Examples include exchange options and call/put options on the maximum or minimum of two assets. Both these well known examples are analyzed in this chapter.

In the BS framework, future prices of X and Y follow correlated geometric Brownian motions. Thus if the prices of the two assets are observed to be x and y at time t, then their future prices at time T > t will have the representation

$\begin{array}{lll}\hfill X_T& \stackrel{d}{=}\hfill & x{e}^{({\mu }_1–\frac{1}{2}{\sigma }_1^2}\hfill \end{array}$