Lesson 5 of 6 · All lessons in this module
  1. Payoff at expiration and exercise value before it
  2. Moneyness: in, at and out of the money
  3. Time value and time value decay
  4. Arbitrage: forwards versus options, and option price boundsVideo lesson
  5. Replication: forwards versus options
  6. Factors that determine an option's valueVideo lesson

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 X(1+r)−TX(1+r)^{-T}, 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.

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