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

A analyst recalibrates a binomial rate tree to a higher volatility assumption while forcing the tree to still reprice the current market zero-coupon curve exactly. Which statement about the effect on model values is correct?

The option-free bond value is unchanged and the callable bond value falls. Calibration to the market curve fixes option-free prices. Higher volatility raises the value of the embedded call that the issuer holds, and the callable bond equals the option-free bond minus that call.

  1. ABoth the option-free bond value and the callable bond value stay unchanged
  2. BThe option-free bond value stays unchanged and the callable bond value fallsCorrect
  3. CThe option-free bond value falls and the callable bond value stays unchanged
  4. DBoth the option-free bond value and the callable bond value fall

Explanation

Because the tree is recalibrated to the market curve, option-free bonds are still priced exactly at their market values. Higher volatility increases the value of the issuer's call option, since optionality is worth more when rates are more dispersed. The callable bond equals the option-free bond minus the call, so its value falls.

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