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

$\begin{array}{lll}\hfill {X}_{T}& \stackrel{d}{=}\hfill & x{e}^{({\mu}_{1}\u2013{\scriptscriptstyle \frac{1}{2}}{\sigma}_{1}^{2}}\hfill \end{array}$

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