CFA Level I · CFA Level I Exam · Option Replication Using Put-Call Parity
An analyst wants to replicate a long call option on a non-dividend-paying stock using put-call parity. Which combination of positions with the same strike and expiry is most appropriate?
A long call is replicated by buying the stock, buying a put and borrowing the present value of the strike, which is a short zero-coupon bond. This follows directly from rearranging put-call parity to c = S + p minus the present value of X.
- AShort stock, long put, long risk-free bond
- BLong stock, long put, short risk-free bondCorrect
- CLong stock, short put, long risk-free bond
Explanation
Parity gives c = S + p - X/(1+r)^T. So a long call equals long stock, long put and borrowing (a short zero-coupon bond with face value X). The option with a short put and long bond would have the wrong signs.
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