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IAI Actuarial Core Principles · Economic Modelling · Principles of option pricing

In a two-period binomial tree, an American put on a non-dividend-paying share is being valued. At an intermediate node, the share price is ₹60, the strike is ₹100, and the continuation value (discounted risk-neutral expectation of next-period option values) is ₹38. What is the option value at that node, and what does it imply?

The node value is ₹40. The American put's value at a node is the larger of immediate exercise payoff (100 − 60 = 40) and continuation value (38). Since exercise exceeds continuation, early exercise is optimal at this node.

  1. A₹38, because American options are never exercised early
  2. B₹40, because early exercise is optimal at this nodeCorrect
  3. C₹40, because early exercise is never optimal for puts
  4. D₹78, being the sum of exercise and continuation values
  5. ₹38, because the put is out of the money

Explanation

At each node an American option is worth the greater of the immediate exercise value and the continuation value. Exercise value = 100 − 60 = 40, which exceeds 38, so the node value is 40 and early exercise is optimal there.

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