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

A share is priced at Rs 100. In one period it moves to either Rs 125 or Rs 80, and the risk-free rate is 10% for the period. A one-period American put has strike K, with K above 80. Above what value of K, to two decimal places, is immediate exercise at time 0 strictly better than waiting?

Early exercise becomes optimal when K exceeds about Rs 108.70. The risk-neutral down probability is one third, so waiting is worth (K-80)/3.3. Setting K-100 greater than (K-80)/3.3 gives K greater than 250/2.3, which is 108.70. Ignoring the discounting would wrongly give 110.

  1. ARs 100.00
  2. BRs 108.70Correct
  3. CRs 110.00
  4. DRs 116.67
  5. Rs 130.77

Explanation

q=(1.1-0.8)/0.45=2/3, so the down probability is 1/3. The put pays 0 after an up-move and K-80 after a down-move, so the continuation value is (1/3)(K-80)/1.1. Exercise is better when K-100>(K-80)/3.3, which gives 3.3K-330>K-80, so K>250/2.3=108.70. Ignoring discounting gives 110, which is the key distractor.

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