Second-order exotic options are perhaps the most direct extension of the simple first-order options considered in the previous chapter. There are two basic types: (a) single asset, two-period exotics which we call dual expiry options (considered in this chapter); and (b) single period, two-asset exotics, commonly referred to as two-asset rainbow options (considered in the next chapter).
As the name implies, the dual expiry options have a payoff structure that depends on the underlying asset price on two future dates T1 and T2 with T1 < T2. Examples, which we analyze in this chapter include: forward start options, compound options, chooser options and several others.
If x1, x2 are the asset prices at times T1 and ...