Theory and Modern Applications
Table 4 Comparison of the American put option values at different underlying values with parameters: \(\sigma=0.3\), \(t=0\), \(T=1\), \(r=0.04\), \(d=0.02\), \(E=100\), \(X=400\)
From: A HODIE finite difference scheme for pricing American options
Stock price x | Binomial method | Analytic approx. method | Compact method 1 | Compact method 2 | Compact method 3 | Our stable scheme | True values |
|---|---|---|---|---|---|---|---|
75.9572 | 25.33949 | 25.4509 | 25.10042 | 25.32570 | 25.32739 | 25.32939 | 25.32986 |
83.9457 | 19.49101 | 19.6617 | 19.34597 | 19.49193 | 19.49383 | 19.49647 | 19.49691 |
92.7743 | 14.27957 | 14.4477 | 14.16375 | 14.25707 | 14.25914 | 14.26231 | 14.26265 |
102.5315 | 9.87092 | 10.0278 | 9.78167 | 9.83789 | 9.84000 | 9.84332 | 9.84354 |
113.3148 | 6.35580 | 6.53401 | 6.32881 | 6.36044 | 6.36241 | 6.36555 | 6.36558 |
125.2323 | 3.84473 | 3.97728 | 3.81244 | 3.82898 | 3.83064 | 3.83327 | 3.83337 |
138.4031 | 2.14801 | 2.25467 | 2.12653 | 2.13452 | 2.13578 | 2.13775 | 2.13784 |