Table 2: Averaged prices of American call options for a range of asset prices .

Method Asset price Black-Scholes formula Growth rate Difference (%) Growth rate Difference (%)

RMEL365.0415.013−0.5555.029−0.238
386.1646.123−0.6656.151−0.211
407.3897.357−0.4337.376−0.176
428.7088.653−0.6328.679−0.333
4410.11210.065−0.46510.092−0.198

Liu10365.0415.0760.6945.0740.655
386.1646.1860.3576.2010.600
407.3897.4260.5017.4580.934
428.7088.7300.2538.7230.172
4410.11210.1690.56410.1580.455

Note: the numbers in the first two columns represent, respectively, asset prices and the corresponding true Black-Scholes prices (as the underlying asset pays no dividend). Columns 3 and 5 report the price estimates with the growth rates of 6% and 100% for the two methods, and each reported value represents an estimate for a particular combination of growth rate and asset price. The values reported in columns 4 and 6 are the corresponding difference between the estimated and the “true” Black-Scholes prices, respectively. The difference is calculated by dividing the estimated price minus the Black-Scholes price by the Black-Scholes price. For both RMEL and Liu10, each reported price estimate is the average of the prices over three independent simulations. In each simulation, 100,000 risk-neutral price paths are generated and each path is divided into exercise opportunities.