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CFA Level I · CFA Level I Exam · Arbitrage, Replication, and the Cost of Carry in Pricing Derivatives

In the pricing of derivatives by replication, an analyst builds a portfolio of the underlying and a risk-free asset that has the same payoff as the derivative in every state. The derivative's price is most likely equal to:

The derivative's price equals the cost of setting up the replicating portfolio. Identical payoffs in every state must have identical prices, otherwise an arbitrageur could buy the cheaper one and sell the dearer one for a riskless profit.

  1. Athe expected payoff discounted at the underlying's required return.
  2. Bthe cost of setting up the replicating portfolio.Correct
  3. Cthe expected payoff of the underlying discounted at the risk-free rate.

Explanation

If two positions have identical payoffs in every state, no-arbitrage requires identical prices. The derivative therefore costs the same as the replicating portfolio. Discounting at the underlying's required return or using real-world expectations ignores this logic.

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