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CFA Level I · CFA Level I Exam · Option Replication Using Put-Call Parity

A share trades at 80. A European call with strike 75 costs 9.00, and a European put with strike 75 costs 2.50 with the same maturity of one year. The annual risk-free rate is 4% (discrete compounding). An analyst wants to replicate a long position in the share using options and a bond. The cost of the bond component and the position used are best described as:

The share is replicated by a long call, a short put and a long risk-free bond costing the discounted strike, 75 divided by 1.04, or 72.12. Rearranging parity gives S = c - p + X/(1+r).

  1. A72.12; long call, short put, long bondCorrect
  2. B72.12; long put, short call, long bond
  3. C75.00; long call, short put, short bond

Explanation

Parity: S = c - p + X/(1+r). Bond cost is 75/1.04 = 72.12. Check: 9.00 - 2.50 + 72.12 = 78.62, which is not 80, so the options are mispriced relative to parity, but the replicating structure is still long call, short put, long bond. Other options reverse the signs or use the undiscounted strike.

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