An Introduction to Special-Purpose Derivatives

This article continues our series on special-purpose derivatives, sometimes known as “exotic” options. Each article in the seriesfocuses on a certain class or type of derivative instrument and discusses several varieties currently being traded. We describe the deJning elements of each instrument and show how the payout is determined. Important applications and primary users are discussed, and, where feasible, closed-form valuation equations are provided. Here we cover three types of special-purpose derivatives whose payouts can depend not only on the final price that is reached on the expiration day, but also on the path the price follows prior to expiration. “Roll up puts” and “roll down calls” contain the provision that if the price of the underlying asset moves against the position past a prespecijed trigger price up in the case of a put, and down for a call the strike price is revised, and the original option turns into a barrier option. That is, when the trigger price is hit, the roll up put’s strike price is raised, but it becomes an up-and-out put, with an outstrike placed at an even higher price. Now i f the underlying asset price continues upward and penetrates the outstrike prior to maturity, the put is cancelled and expires worthless, regardless ofwhat happens to the asset price aJer that point. Similarly, a roll down call becomes a down-and-out call aJer the trigger price is hit. In its simplest form, a contingent premium option is like a regular option except that no premium is paid at the outset. The optionholder pays nothing until expiration, and then only ifthe option is in the money. As Kat describes in another article in this journal, many other types ofcontingent premium contracts are also possible.