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CFA Level I · CFA Level I Exam · Arbitrage, Replication, and the Cost of Carry in Pricing Derivatives

A stock is at 50 and will be either 60 or 40 after one period. The risk-free rate is 5% per period. A call option with a strike of 50 is replicated by buying shares and borrowing at the risk-free rate. The call's value today is closest to:

The call is worth about 5.95, which is not listed as such; none of the choices match the replication result, so the keyed choice is not valid.

  1. A3.57
  2. B4.76Correct
  3. C5.00

Explanation

Payoffs are 10 up and 0 down. Hedge ratio = 10/(60−40) = 0.5 shares. Down state: 0.5×40 = 20 equals the loan repayment, so the loan is 20/1.05 = 19.05. Cost = 0.5×50 − 19.05 = 5.95? Recheck: replicate call, up: 0.5×60 − 20 = 10, down: 20 − 20 = 0, correct. Value = 25 − 19.05 = 5.95. Risk-neutral check: p = (1.05×50 − 40)/20 = 0.625; value = 0.625×10/1.05 = 5.95.

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