Abstract:

We analyzed American lookback call option valuation problem. Using the variable mesh finite element algorithm, we obtained the discrete form of the BlackScholes equation, which is used to determine the value of American lookback option. Furthermore, we got the optimal exercise boundary using the Newton iterative method. When the two methods were alternately used, we gave corresponding numerical solutions. Finally, compared with the binomial method,
this method is efficient and the theoretical analysis.

Key words: American lookback call option, variable mesh finite element algorithm, optimal exercise boundary