Delta Across the Tree

Rebalancing

A delta hedge must be rebalanced each step as delta changes.

highlighted = computed this step

Rebalancing the hedge

Because delta changes from 13/21 share today to a different value at the next step, a hedge set today must be rebalanced to the new delta. This dynamic rebalancing keeps the position riskless one step at a time.

Δtoday→Δnext step\Delta_{\text{today}}\to\Delta_{\text{next step}}

Model note

Rebalancing is costless only under the frictionless assumptions; real trading has transaction costs. This is descriptive, not investment advice.

frictionless rebalancing\text{frictionless rebalancing}