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.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

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}