A lookback put gives the owner the right to sell the underlying at expiry at a strike price equal to the highest price that spot traded over the life of the option. Lookbacks are expensive. Anything that gives you the right to pick the top or the bottom is going to be costly. The strike price on the compound is the premium that we would pay in 1 month's time if we exercised the compound for the option expiring 6 months from that point in time. These types of products are often used by corporations to hedge the foreign exchange risk involved with overseas acquisitions when the success of the acquisition itself is uncertain.
Sophisticated speculators use compound options to speculate on the volatility of volatility.
We will discuss that in a subsequent article.