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

In a multi-period binomial model, an American put on a non-dividend-paying share is valued by backward induction. At an interior node, which comparison determines the option value?

The node value is the larger of the immediate exercise payoff and the discounted risk-neutral expectation of the next-step option values, because the American holder can choose to exercise early or continue holding.

  1. AThe larger of the immediate exercise value and the discounted risk-neutral expected value of the next-step option valuesCorrect
  2. BThe smaller of the immediate exercise value and the discounted expected value
  3. CThe discounted expected share price minus the strike
  4. DThe immediate exercise value only, as early exercise is always optimal
  5. The discounted expected value only, as early exercise is never optimal

Explanation

At each node the holder chooses between exercising now and continuing. Value is the maximum of the intrinsic value and the discounted risk-neutral expectation of the successor node values. For puts early exercise can be optimal, so neither extreme option is right.

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