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FRM Part I · FRM Exam Part I · Binomial Trees

For an American put on a non-dividend-paying stock valued on a binomial tree, which set of conditions makes early exercise at a given node more likely?

Early exercise is more likely when the put is deep in the money, interest rates are high and volatility is low. Receiving the strike sooner earns interest, and there is little time value to sacrifice. High volatility or zero rates make waiting more valuable.

  1. AThe put is deep out of the money, interest rates are low and volatility is high
  2. BThe put is deep in the money, interest rates are high and volatility is lowCorrect
  3. CThe put is at the money, interest rates are zero and volatility is high
  4. DThe put is deep in the money, interest rates are zero and volatility is low

Explanation

Early exercise of a put brings forward the strike cash, which earns interest, so higher rates favour it. A deep in-the-money put has little time value left to give up. Low volatility reduces the time value from further favourable moves. With zero rates there is no benefit from receiving the strike early, so the final option fails on that count.

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