The article concerns the quantile hedging of an European option in the Cox-Rubinstein model. After introducing the problem of hedging a derivative instrument, two problems of quantile hedging were formulated. Then, using the method based on a martingale measure, the optimal success coefficient for hedging European option were derived. Finally, the results of empirical research concerning the quality of the quantile hedging the warrants from the Polish stock market were given. In this empirical research the Monte Carlo method with the bootstrap samples was used
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