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

A risk manager prices bonds on a calibrated binomial tree using risk-neutral probabilities of 0.5. A research team then argues that the real-world probability of the rate rising is 0.7, not 0.5, and asks for the tree prices to be revised. The tree's rates and the market prices used for calibration stay unchanged. What is the correct response?

Prices should not change. In an arbitrage-pricing tree, values are fixed by replication and calibrated risk-neutral probabilities, so real-world views on rate direction do not enter. Those views affect expected returns and the risk premium. Using 0.7 for pricing would make the model inconsistent with the calibrating market prices.

  1. AArbitrage-free prices stay the same, because replication fixes prices without reference to real-world probabilitiesCorrect
  2. BPrices should fall, because a higher up-rate probability raises expected discount rates
  3. CPrices should rise, because higher real-world volatility raises convexity value
  4. DPrices should be recomputed with 0.7 only for the options and 0.5 for the bonds

Explanation

Arbitrage-free prices come from replicating each payoff with traded securities, so they depend on the tree's rates and the risk-neutral probabilities implied by market prices. Real-world probabilities affect expected returns and the risk premium, not the arbitrage price. Replacing 0.5 by 0.7 in pricing would break consistency with the calibration prices and create arbitrage opportunities within the model.

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