IAI Actuarial Core Principles · Economic Modelling · Binomial option-pricing model
In a two-period tree with per-period risk-free growth 1+r, the replicating portfolio for an option at time 0 holds Δ shares. Which statement about Δ is correct?
Δ is recalculated at every node as the difference in successor option values divided by the difference in successor share prices, so the hedge is rebalanced dynamically as the tree evolves.
- AΔ is fixed for the whole life of the option
- BΔ equals the risk-neutral probability q
- CΔ is recalculated at each node as the difference in the option values divided by the difference in share prices at the successor nodesCorrect
- DΔ equals the option price divided by the share price
- Δ is always between -1 and 0 for a call
Explanation
Replication is dynamic: at each node Δ = (Vu - Vd)/(Su - Sd) using the successor nodes. It changes along the tree, so it is not fixed. It is not q, and for a call it lies between 0 and 1.
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