CFA Level I · CFA Level I Exam · Option Replication Using Put-Call Parity
Put-call parity for European options on a non-dividend-paying stock is rearranged to isolate the risk-free bond. A long position in a risk-free bond with face value equal to the strike is most likely replicated by:
The bond is replicated by holding the stock, buying a put and writing a call at the same strike and expiry. Put-call parity shows this portfolio always pays the strike at expiry, which is the payoff of a risk-free zero-coupon bond.
- Along call, short put, short stock
- Blong stock, long put, short callCorrect
- Clong stock, long call, short put
Explanation
From S + p - c = X/(1+r)^T, the bond equals long stock, long put and short call. This is a covered-call-with-put (conversion) structure with fixed payoff X. The other options give variable payoffs.
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