Weak Convergence for Approximation of American Option Prices

Based on a sequence of discretized American option price processes under the multinomial model proposed by Maller, Solomon and Szimayer [12], the sequence converges to the counterpart under the original Lévy process in distribution for almost all time. By adapting Skorokhod representation theorem, a new sequence of approximating processes with the s ame laws with the multinomial tree model defined by Maller, Solomon and Szimayer [12] is obtained. The new sequence satisfies Aldous’ criterion for tightness, and the sequence of filtrations generated by the new approximation converges to the filtration generated by the representative of Lévy process weakly. By using results of Coquet and Toldo [5], we give a complete proof of the weak convergence for the approximation of American put option prices for all time. Hence the numerical approximation can be adapted in practice.