Approximating the exact value of an American option


  • Stefano Herzel Università degli Studi di Perugia



An American option is a derivative security that can be exercised at any time before expiration. Under standard hypotheses it can be shown that its arbitrage-free price is the solution of an optimal stopping problem. Usually, if the underlying asset follows a diffusion, the stopping time problem does not have a closed form solution. Therefore, discrete time models have been proposed to determine an approximated solution. I formulate some conditions on the discrete process to insure convergence of the approximations to the exact value. I also show how to apply such conditions to check the correctness of some of the most popular discretization schemes.


How to Cite

Herzel, S. (2004). Approximating the exact value of an American option. Statistica, 64(2), 287–304.