Pricing Outside Floating-Strike Lookback Options

A floating-strike lookback call option gives the holder the right to buy at the lowest price of the underlying asset. Similarly, a floating-strike lookback put option gives the holder the right to sell at the highest price. This paper will propose an outside floating-strike lookback call (or put) option that gives the holder the right to buy (or sell) one underlying asset at some percentage of the lowest (or highest) price of the other underlying asset. In addition, this paper will derive explicit pricing formulas for these outside floating-strike lookback options. Sections 3 and 4 assume that the underlying assets pay no dividends. In contrast, Section 5 will derive explicit pricing formulas for these options when their underlying assets pay dividends continuously at a rate proportional to their prices. Some numerical examples will be discussed.