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

In a risk-neutral binomial tree calibrated to today's zero-coupon curve, a risk manager notices that the model price of a 2-period bond is higher than the observed market price while the 1-period bond matches. Which adjustment correctly restores arbitrage-free calibration?

Raise the rate drift at the second-period nodes. A model price above the market price means the tree's rates are too low. Shifting the rates up increases discounting and lowers the model bond price until it equals the market price.

  1. ARaise the drift (the rate level) at the second-period nodes so discounting is heavierCorrect
  2. BLower the volatility so convexity is smaller
  3. CLower the risk-neutral probability of the up move without changing rates
  4. DShorten the time step so the tree has more periods

Explanation

A model bond price that is too high means rates in the tree are too low. Increasing the drift (shifting rates up at the relevant date) lowers the discounted expected value and matches the market price. Lowering volatility would increase the price further through convexity effects (convexity raises bond value); the other options do not target the date-specific fit.

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