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

A European call and a European put have the same underlying, strike and expiration. Under put-call parity with no arbitrage, the combination of a long call and a short put is most likely equivalent to:

A long call plus a short put replicates a leveraged long position in the underlying: owning the asset financed by borrowing the present value of the exercise price. This follows from rearranging put-call parity to c - p = S0 - X/(1+r)^T.

  1. Aa long position in the underlying financed by borrowing the present value of the exercise priceCorrect
  2. Ba short position in the underlying combined with a long position in a risk-free bond
  3. Ca long position in the underlying combined with a long position in a risk-free bond

Explanation

Put-call parity is c - p = S0 - X/(1+r)^T. A long call plus a short put therefore replicates owning the underlying while borrowing the present value of X. The other choices have the wrong sign on the underlying or the bond.

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