Lesson 5 of 6 · 11 min
Replication: forwards versus options
Like a forward, an option can be copied with the underlying and risk-free borrowing or lending, but because exercise is uncertain, the copy uses only part of PV(X) and must be adjusted over time.
In short
- Replication creates a derivative's cash flows from the underlying plus risk-free borrowing or lending; it keeps the law of one price in force.
- Long call replica: borrow at the risk-free rate and buy the underlying.
- Long put replica: short the underlying and lend the proceeds at the risk-free rate.
- If exercise were certain you would borrow (call) or lend (put) the full , as for a forward. Since it is not, you use a proportion tied to the likelihood of exercise.
- A forward's replicating trades stay fixed; an option's must be adjusted as the likelihood of exercise (moneyness) changes.
Unlock this lesson free for 7 days
Create a free account to get 7 days of full access — every lesson, video, flashcard, mock and the question bank. No card needed.