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FRM Part II · FRM Exam Part II · Arbitrage Pricing with Term Structure Models

A trader builds a portfolio of traded securities whose payoffs match those of a derivative in every future state of the world. Under the no-arbitrage principle, what must be true of the derivative's price today?

The derivative must be priced at the cost of the replicating portfolio. Identical payoffs in every state mean any price gap would allow a riskless profit by buying the cheap position and selling the expensive one. Risk preferences do not enter the relationship.

  1. AIt must equal the cost of setting up the replicating portfolio today.Correct
  2. BIt must equal the expected payoff under real-world probabilities discounted at the risk-free rate.
  3. CIt must be higher than the replicating portfolio cost, to compensate the seller for risk.
  4. DIt may differ from the replicating portfolio cost if investors are sufficiently risk averse.

Explanation

If two positions have identical payoffs in every state, any price difference lets an arbitrageur buy the cheaper and sell the dearer for a riskless profit. So the derivative's price must equal the replicating portfolio's cost. Risk aversion and real-world probabilities play no role in this relationship.

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