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IAI Actuarial Core Principles · Economic Modelling · Binomial option-pricing model

In a binomial model for a non-dividend-paying share with a positive interest rate, which statement correctly explains why an American put may be exercised early at a deep in-the-money node?

A deep in-the-money American put may be exercised early because receiving the strike now lets it earn interest. The remaining time value of waiting can be smaller than this interest, since the payoff is capped at the strike. This is why American puts can be worth more than European puts.

  1. AThe strike received immediately can earn interest, and this can outweigh the remaining time value of the putCorrect
  2. BThe put has a negative delta, so waiting always lowers its value
  3. CThe risk-neutral probability of a down-move exceeds one half at such nodes
  4. DThe American put value must equal the European put value at every node
  5. Early exercise removes volatility risk, which has a positive value for put holders

Explanation

For a deep in-the-money put the upside from waiting is small, because the payoff cannot exceed K. Receiving K now and earning interest can then be worth more than the discounted expected payoff. The risk-neutral probabilities do not depend on the node and have no link to moneyness. Put-call parity-style equality of American and European puts does not hold, because the early exercise premium is positive.

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