American vs European

The Early-Exercise Premium

The extra exercise right creates an early-exercise premium.

highlighted = computed this step

European comparison

The European put with the same tree cannot exercise early. Its rounded value is $5.44, exact 800/147 dollars.

VE=800/147≈$5.44V_E=800/147\approx \$5.44
American put comparisonThe American put value and exercise decision are recomputed.updowntodayS $100.00V $7.14exerciset1 u0S $90.00V $15.00t1 u1S $120.00V $0.00t2 u0S $81.00V $24.00t2 u1S $108.00V $0.00t2 u2S $144.00V $0.00

Premium

The American put is rounded $7.14, exact 50/7 dollars. The early-exercise premium is the difference: rounded $1.70, exact 250/147 dollars.

premium=VA−VE=250/147≈$1.70\text{premium}=V_A-V_E=250/147\approx \$1.70

Never negative

The right to exercise early is never worth less than zero, because the holder can always choose not to use it. In this model, American value is at least European value.

VA≥VEV_A\ge V_E