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

Which position most likely replicates a long zero-coupon risk-free bond with face value equal to the strike, using only the underlying stock and options with that strike and expiry?

A long stock, long put and short call position replicates the risk-free bond, since X/(1+r)^T = S + p - c. Whatever the final stock price, the payoff equals the strike, so the position is riskless.

  1. ALong stock, long put, short callCorrect
  2. BLong stock, short put, long call
  3. CShort stock, long put, long call

Explanation

From parity, X/(1+r)^T = S + p - c. That is long stock, long put and short call (a conversion). The other combinations give synthetic stock-related or put-related exposures rather than a riskless payoff of X.

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