Optimal Algorithms for k-Search with Application in Option Pricing

Authors:
Julian Lorenz;Konstantinos Panagiotou;Angelika Steger
Affiliations:
ETH Zurich, Institute of Theoretical Computer Science, 8092, Zurich, Switzerland;ETH Zurich, Institute of Theoretical Computer Science, 8092, Zurich, Switzerland;ETH Zurich, Institute of Theoretical Computer Science, 8092, Zurich, Switzerland
Venue:
Algorithmica - Special Issue: European Symposium on Algorithms 2007, Guest Editors: Larse Arge and Emo Welzl
Year:
2009

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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 worst-case. 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.