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

Under put-call parity for European options on a non-dividend-paying stock, a long position in the stock combined with a long put and a short call, all with the same strike and expiration, most likely replicates a position in:

The portfolio of long stock, long put and short call has a payoff equal to the strike price in all scenarios. That is the payoff of a risk-free zero-coupon bond with face value equal to the strike, so it replicates that bond.

  1. Aa zero-coupon bond with face value equal to the strike priceCorrect
  2. Ba long forward contract on the stock with zero value
  3. Ca short position in the underlying stock

Explanation

Parity states S + p = c + X/(1+r)^T. Rearranging gives S + p - c = X/(1+r)^T. The portfolio payoff is X at expiration in every state, which is a risk-free zero-coupon bond paying the strike. The forward does not match, since a forward's payoff varies with the stock price.

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