Valuing the American Put

A Node Where You Exercise

Early exercise matters when intrinsic value beats continuation value.

highlighted = computed this step

Down node

At the first down node, the stock is $90.00. Holding gives rounded $11.43, exact 80/7 dollars, while exercising gives $15.00.

Cd=1/2⋅$0.00+(1−1/2)⋅$24.001+r=80/7≈$11.43C_d=\frac{1/2\cdot \$0.00+(1 - 1/2)\cdot \$24.00}{1+r}=80/7\approx \$11.43
American put rollbackThe 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

Exercise wins

Immediate exercise is larger than holding. The American rule marks this node for exercise and uses $15.00 as the node value.

Vd=max⁡($15.00,80/7)=$15.00V_d=\max(\$15.00,80/7)=\$15.00

Local decision

Only this interior node exercises in the worked tree. Terminal payoff nodes are payoff outcomes, not early-exercise decisions.

exercise where intrinsic exceeds continuation\text{exercise where intrinsic exceeds continuation}