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

In a one-period binomial model, an analyst prices a derivative by building a portfolio of the underlying and a risk-free bond that replicates its payoffs. The derivative's price today is most likely equal to:

The derivative's price equals the cost today of the replicating portfolio. Because the portfolio produces identical payoffs in every state, any other price would allow arbitrage. Simple averaging or discounting at the underlying's required return is not how replication pricing works.

  1. Athe expected payoff discounted at the underlying's required return
  2. Bthe present value of the replicating portfolio's cost todayCorrect
  3. Cthe average of the up and down payoffs discounted at the risk-free rate

Explanation

If a portfolio replicates the derivative's payoffs in every state, no-arbitrage requires the derivative to cost the same as that portfolio today. Discounting the real-world expected payoff at the underlying's required return, or taking a simple average of payoffs, ignores the actual state probabilities needed for risk-neutral pricing.

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