Optimal algorithms for k-search with application in option pricing

Authors:
Julian Lorenz;Konstantinos Panagiotou;Angelika Steger
Affiliations:
Institute of Theoretical Computer Science, ETH Zurich, Zurich, Switzerland;Institute of Theoretical Computer Science, ETH Zurich, Zurich, Switzerland;Institute of Theoretical Computer Science, ETH Zurich, Zurich, Switzerland
Venue:
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Year:
2007

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Abstract

In the k-search problem, a player is searching for the k highest (respectively, lowest) prices in a sequence, which is revealed to her sequentially. At each quotation, the player has to decide immediately whether to accept the price or not. Using the competitive ratio as a performance measure, we give optimal deterministic and randomized algorithms for both the maximization and minimization problems, and discover that the problems behave substantially different in the worstcase. As an application of our results, we use these algorithms to price "lookback options", a particular class of financial derivatives. We derive bounds for the price of these securities under a no-arbitrage assumption, and compare this to classical option pricing.