Early Exercise

Exercise or Hold

At each node, the model compares exercise now with holding.

highlighted = computed this step

The node choice

At a node, compare intrinsic value from exercise now with continuation value from holding. The holder takes the larger value.

V=max⁡(intrinsic,continuation)V=\max(\text{intrinsic},\text{continuation})
American put treeThe 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

Put intrinsic value

For a put, intrinsic value is strike minus stock when that is positive, otherwise zero.

intrinsic=max⁡(K−S,0)\text{intrinsic}=\max(K-S,0)

Continuation value

Continuation is the discounted risk-neutral value of the next up and down option values.

continuation=qVu+(1−q)Vd1+r\text{continuation}=\frac{qV_u+(1-q)V_d}{1+r}

Model note

Exercise-or-hold values are model values under the stated binomial assumptions, not market prices. The model is frictionless and uses no transaction costs, fees, taxes, credit risk, liquidity limits, or default. This is descriptive, not investment advice.

exercise rule is model-based\text{exercise rule is model-based}