Regret Minimization Algorithms for Pricing Lookback Options
Abstract
In this work, we extend the applicability of regret minimization to pricing financial instruments, following the work of [11]. More specifically, we consider pricing a type of exotic option called a 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.
Cite
Text
Gofer and Mansour. "Regret Minimization Algorithms for Pricing Lookback Options." International Conference on Algorithmic Learning Theory, 2011. doi:10.1007/978-3-642-24412-4_20Markdown
[Gofer and Mansour. "Regret Minimization Algorithms for Pricing Lookback Options." International Conference on Algorithmic Learning Theory, 2011.](https://mlanthology.org/alt/2011/gofer2011alt-regret/) doi:10.1007/978-3-642-24412-4_20BibTeX
@inproceedings{gofer2011alt-regret,
title = {{Regret Minimization Algorithms for Pricing Lookback Options}},
author = {Gofer, Eyal and Mansour, Yishay},
booktitle = {International Conference on Algorithmic Learning Theory},
year = {2011},
pages = {234-248},
doi = {10.1007/978-3-642-24412-4_20},
url = {https://mlanthology.org/alt/2011/gofer2011alt-regret/}
}