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FRM Part I · FRM Exam Part I · Binomial Trees

An American call option is written on a stock that will pay one large cash dividend during the option's life. In a binomial tree that models this dividend, at which point might early exercise of the call be optimal?

Early exercise of an American call on a dividend-paying stock can be optimal only immediately before an ex-dividend date. It makes sense only if the dividend captured is large enough to exceed the time value surrendered and the interest lost on the strike.

  1. AImmediately after the ex-dividend date, once the stock price has dropped
  2. BAt any node before the ex-dividend date regardless of the dividend size, since the call is always in the money
  3. COnly at expiry, because dividends never affect early exercise of calls
  4. DImmediately before the ex-dividend date, if the dividend is large enough to outweigh the lost time value and the interest on the strikeCorrect

Explanation

Exercising just before the ex-dividend date lets the holder receive the dividend. This is worthwhile only if the dividend exceeds the time value lost plus the interest forgone on the strike. After the ex-dividend date the stock price falls and the benefit is gone. Without a dividend, early exercise of a call is not optimal.

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