Arbitrage-free

Priced so that no riskless profit is available from combining it with other instruments. An arbitrage-free rate tree or model is one fitted to reproduce the market prices of benchmark bonds.

Where you will meet it

Arbitrage-free appears in 6 learning outcomes on the CFA syllabus. A few of them:

• Value a bond by discounting at spot rates
  CFA Level I · Fixed Income

  “Pricing with spot rates discounts each cash flow at the rate appropriate to its own date, which is the arbitrage-free value: any other price could be exploited by stripping the bond into its component payments or reconstituting it from them.”

• Explain the idea of valuing a fixed-income instrument so that no arbitrage is possible
  CFA Level II · Fixed Income

  “An arbitrage-free value is the price that leaves no riskless profit available.”

• Use a two-period binomial model to value an interest rate option and explain the result
  CFA Level II · Derivatives and Risk Management

  “Interest rate options use an arbitrage-free tree of one-period rates, with probabilities of 0.5 on each branch.”

• Explain how a Monte Carlo simulation of forward rates works and where it is applied
  CFA Level II · Fixed Income

  “The model must first be made arbitrage-free: if it misprices benchmark bonds, a constant drift adjustment is added to the simulated rates until those bonds are priced correctly.”

Practise it

• Today's practice question One question, with every wrong option explained.
• Free Level I diagnostic test Twelve questions that show which topics to start with.
• Free finance calculators Check your arithmetic on the exam's core formulas.

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