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FRM Part I · FRM Exam Part I · Properties of Options

An analyst holds a long European call and a short European put on a non-dividend-paying stock, both with the same strike K and expiry T. Which position does this portfolio replicate?

The portfolio replicates a long stock position financed by borrowing the present value of the strike. Put-call parity gives c - p = S0 - K e^(-rT), and the payoff at expiry is S_T - K whether the stock finishes above or below K.

  1. ALong one share of stock financed by borrowing the present value of KCorrect
  2. BLong one share of stock financed by borrowing K at expiry with no discounting
  3. CShort one share of stock and lending the present value of K
  4. DLong one share of stock and lending the present value of K

Explanation

Parity gives c - p = S0 - K e^(-rT). Long call, short put equals long stock plus a borrowing whose repayment at T is K, with present value K e^(-rT). The payoff is S_T - K in all outcomes. The short stock and lending alternative is the opposite position.

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