Regret Minimization Algorithms for Pricing Lookback Options
Eyal Gofer and Yishay Mansour
In: The 22nd International Conference on Algorithmic Learning Theory, October 5 - 7, 2011, Espoo, Finland.

Abstract

In this work, we extend the applicability of regret minimization to pricing financial instruments, following the work of [10]. More specifically, we consider pricing a type of exotic option called a {\it fixed-strike lookback call option}. A fixed-strike lookback call option has a known expiration time, at which the option holder has the right to receive the difference between the maximal price of a stock and some pre-agreed price. We derive upper bounds on the price of these options, assuming an arbitrage-free market, by developing two-way trading algorithms. We construct our trading algorithms by combining regret minimization algorithms and one-way trading algorithms. Our model assumes upper bounds on the absolute daily returns, overall quadratic variation, and stock price, otherwise allowing for fully adversarial market behavior.

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