ABSTRACT
Exotic options are contracts that depend on three or more underlying assets. We have already studied lookback options that depend on a stock S, a bond BT (or equivalently a dollar $), and on the maximal asset M∗. The maximal asset itself depends on the stock and the bond, so it is not a free asset that exists on its own. This chapter studies contracts on three “full” underlying assets; let us call them X , Y , and Z. There are several variants of these contracts. A quanto is a contract that pays off some function of the price of XY (T ) units of the third asset Z. The underlying assets for quanto contracts are usually currencies, but the definition is not limited to them. For example, a quanto forward pays offXY (T )−K units of Z, and a quanto call option pays off (XY (T )−K)+ units of Z. The quanto contracts have only one underlying price process, but the option is settled in a “wrong” asset. A contract that depends on three or more assets and two or more price processes is known as a rainbow option. The price of a rainbow option thus depends on the joint distribution of two or more price processes, and they are sensitive to the correlation structure of the prices. Some rainbow option contracts are known under a specific name, for instance a call option on the maximum of two assets, etc. We call them “the friends of quantos and rainbows.”
