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FRM Part I · FRM Exam Part I · Binomial Trees

For an American put on a non-dividend-paying stock, holding the other inputs fixed, which statement about the incentive to exercise early at a given in-the-money node is correct?

Early exercise of an American put is more attractive when interest rates are higher and volatility is lower. Exercising brings in the strike cash earlier, so a higher rate raises its value, while lower volatility reduces the time value given up by exercising.

  1. AEarly exercise becomes more attractive when interest rates are lower and volatility is higher
  2. BEarly exercise becomes more attractive when interest rates are higher and volatility is lowerCorrect
  3. CThe interest rate has no bearing, because the exercise decision depends only on intrinsic value
  4. DEarly exercise is never optimal for a put, because it forfeits time value and interest on the strike

Explanation

Exercising a put brings in the strike now, and the cash can earn interest, so a higher rate raises the benefit of exercising early. Lower volatility reduces the time value of waiting, which also favors exercise. Unlike a call on a non-dividend stock, a put can be optimally exercised early, especially when deep in the money.

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