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 exact 50/7 dollars, displayed as $7.14, 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.todaydownupS $100.00V $7.14S $90.00V $15.00S $120.00V $0.00S $81.00V $24.00S $108.00V $0.00S $144.00V $0.00

Hold wins

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

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 and American put value are model outputs under the stated constant-move, one-rate, frictionless assumptions, not market prices. The model ignores transaction costs, fees, taxes, credit risk, liquidity limits, and default. Changing the model inputs can move which nodes exercise. This is descriptive, not investment advice.

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