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

A trader replicates a one-period bond option using a bond and cash in a binomial tree. The replicating portfolio costs 2.40, while the option trades at 2.70 in the market. Which action locks in an arbitrage profit?

Sell the overpriced option at 2.70 and buy the replicating portfolio for 2.40. Their payoffs match in every state, so the 0.30 difference is a riskless profit. Buying the option would instead lock in a loss.

  1. ASell the option and buy the replicating portfolioCorrect
  2. BBuy the option and sell the replicating portfolio
  3. CBuy both the option and the replicating portfolio
  4. DSell both and invest proceeds at the risk-free rate

Explanation

The option is overpriced by 0.30 relative to its replicating cost. Selling the option at 2.70 and buying the replicating portfolio for 2.40 gives a riskless profit of 0.30 because payoffs offset in every state.

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