Double-barrier lookback options

While lookback options offer the advantages of mitigating market timing risks and maximizing profits by allowing investors to buy at the lowest price or sell at the highest price of the underlying asset, they have the obvious drawback of high prices. One way to lower the price of lookback options is to introduce barriers to the payoff structure. This intention has led to the development of lookback options with various types of barriers: full or partial, single or double, constant or time-varying. Although lookback options with barriers have been studied in the literature for several decades, no pricing formula has been given for lookback options with double barriers. Here, we extend the scope of lookback-barrier options by providing pricing formulas for lookback options with double barriers. Like many previous studies, we assume that the lookback monitoring period and the barrier period are non-overlapping. However, while previous studies only consider the front-end barrier cases where the lookback monitoring period follows the barrier period, our method can also handle the rear-end barrier case where the lookback monitoring period precedes the barrier period. In addition, we conducted numerical experiments to verify the accuracy of the derived formulas by comparing the formula-based prices with those obtained from Monte Carlo simulations. Furthermore, we compared numerically the limiting cases of our formulas with the prices of front-end single-barrier fixed-strike lookback options and no-barrier fixed-strike lookback options, as reported in the existing literature.