Valuing the American Put

Rolling Back

The same max rule rolls the tree back to today.

highlighted = computed this step

Continue at the root

The first up node is worth $0.00. At today's node, holding gives rounded $7.14, exact 50/7 dollars, while exercise value is $5.00.

C0=1/2⋅$0.00+(1−1/2)⋅$15.001+r=50/7≈$7.14C_0=\frac{1/2\cdot \$0.00+(1 - 1/2)\cdot \$15.00}{1+r}=50/7\approx \$7.14
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

Hold wins

Holding is larger than exercising, so the root is held and the American put price is rounded $7.14, exact 50/7 dollars.

V0=max⁡($5.00,50/7)=50/7≈$7.14V_0=\max(\$5.00,50/7)=50/7\approx \$7.14

Model note

The exercise decision is local to each node. Changing the model inputs can move which nodes exercise.

exercise set depends on the model inputs\text{exercise set depends on the model inputs}