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FRM Part I · FRM Exam Part I · Properties of Options

An American put on a non-dividend-paying stock has strike 50. The stock price has fallen to 2 and the risk-free rate is 6% per year. Which statement best explains why early exercise may be optimal?

Early exercise of a deep in-the-money American put can be optimal because the stock price can fall only a little further, while receiving the strike now lets the holder earn interest on the cash. That interest can outweigh the small remaining time value.

  1. AThe put is deep in the money, so receiving the strike now and earning interest on it can outweigh the remaining time valueCorrect
  2. BExercising a put early avoids paying dividends on the stock
  3. CA put should always be exercised early when volatility is above the risk-free rate
  4. DThe put's value cannot fall below the strike price at any time

Explanation

For a deep in-the-money put, the maximum further gain is limited because the stock cannot fall below zero, while receiving K=50 now allows interest to accrue. Therefore the benefit of waiting is small compared with interest earned on the proceeds. The dividend option is wrong because the stock pays none and put holders do not pay dividends.

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