The article describes a simulative approach to the valuation of a non-standard option contract which hedges a long position resulting from an investment made on the Warsaw Stock Exchange. On the basis of empirical data, the author presents the methodology of selecting a reliable process to generate the price of the hedged instrument. Next steps include a definition of the barrier option withdrawal function adopted to the needs of a hypothetical investor and the simulation of a contract valuation accompanied by considerations with respect to its effectiveness. The author shows how a selection of an appropriately defined exotic option may reduce the costs of hedging an open position.

Historical values of the WIG20 index indicate that assumptions on the normal rate of return on shares, which underly classical models of derivative valuation should be rejected. As an alternative, Levy's process was proposed, based on stationary and independent growths with hyperbolic spreads. Judging by the results of the simulation, one may say that the adoption of classical assumptions as to the normal rate of return on shares leads to a rather distinct overestimation in the value of an option contract, which is also noticeable in the valuation of a standard option. This overestimate may be markedly increased owing to the application of complicated pay-out functions typical for exotic options.