CFA Level I · CFA Level I Exam · Option Replication Using Put-Call Parity
Using put-call parity for European options on a non-dividend-paying stock, a long position in the stock combined with a long put (same strike and expiry) most likely replicates which of the following?
A stock plus a put equals a long call plus a long zero-coupon bond with face value equal to the strike, because put-call parity states S + p = c + X/(1+r)^T. The bond leg is held long, not shorted.
- AA short call plus a long risk-free bond
- BA long call plus a long zero-coupon bond with face value equal to the strikeCorrect
- CA long call plus a short position in the zero-coupon bond
Explanation
Put-call parity: S + p = c + X/(1+r)^T. A protective put (stock plus put) equals a long call plus a long zero-coupon bond whose face value is the strike. The short-bond version would reverse the sign of the bond leg.
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