Delta Across the Tree

Delta Changes

The hedge ratio is different at every node of the tree.

highlighted = computed this step

Delta is not constant

The hedge ratio differs at every node. At the up node it is 1 share; at the down node it is 1/9 share. Delta rises toward a full share as the option moves in the money and falls toward zero as it moves out of the money.

Δu=1,Δd=1/9\Delta_u=1,\quad \Delta_d=1/9
Binomial treeStock and call values are recomputed at every node.todaydownupS $100.00V $10.20S $90.00V $1.43S $120.00V $20.00S $81.00V $0.00S $108.00V $3.00S $144.00V $39.00

Model note

Each node's delta is exact in the stated binomial model with constant move factors, one stated rate, and frictionless trading. This is descriptive, not investment advice.

delta varies by node\text{delta varies by node}