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

In a binomial tree, the holder of an American put compares, at each node, the value from exercising now with the value from continuing. Which statement describes the correct backward-induction rule?

At each node the American option value is the larger of the immediate exercise payoff and the discounted risk-neutral expected value of the following nodes, working backwards from expiry.

  1. AValue at a node is the maximum of the immediate exercise payoff and the discounted risk-neutral expectation of the next-step valuesCorrect
  2. BValue at a node is the minimum of the immediate exercise payoff and the discounted risk-neutral expectation of the next-step values
  3. CValue at a node is the discounted expectation of next-step values only, with exercise considered at expiry alone
  4. DValue at a node is the immediate exercise payoff whenever it is positive, otherwise zero
  5. Value at a node is the average of the exercise payoff and the continuation value

Explanation

The holder chooses the better of exercising and continuing, so the node value is the maximum of the intrinsic value and the discounted risk-neutral expected value of the next step. Taking the minimum or the average understates the value, and ignoring continuation is wrong because holding can be worth more. Using only the discounted expectation describes a European option.

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