Which of the following can be used to create a long position in a European put option on a stock?

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BlackTom AI · Accepted Answer

We need to analyze how to construct a portfolio that delivers the payoff of a long European put on a stock.
Option a: Buy a call on the stock, sell the stock, and deposit K e^(-r(T-t)) in the bank. This matches the put-call parity rearrangement P = C − S + K e^(−rT). Here you hold a long call (C), you are short the stock (−S), and you place K e^(−rT) in cash (a risk-free bond) to mature at K at time T. Together, this combination replicates a long put payoff at expiration. This option is consistent with the standard replication and is therefore correct.
Option b: Sell a call, buy the stock, and borrow K e^(−r(T-t)) from the bank. This would correspond to a different combination, not the standard parity for a long put. Selling a call with owning the stock can create a different synthetic position (a covered call plus debt), not the long put payoff. The borrow amount also changes the cash-flow profile away from the put replication.
Option c: Sell a call, sell the stock, and deposit K e^(−r(T-t)) in the bank. This would produce a very different payoff pattern, essentially aligning with a short call and a short stock position funded by cash, which does not replicate a long put. The signs of the positions do not match the put parity relationship needed for a long put.
Option d: Buy a call, buy the stock, and borrow K e^(−r(T-t)) from the bank. This creates a net long stock plus call position with a liability (borrowed cash) that does not align with the put’s payoff structure. It does not implement the P = C − S + Ke^(−rT) relation and thus fails to replicate a long put.

FINS3635-Options, Futures & Risk Mgmt - T3 2025

Which of the following can be used to create a long position in a European put option on a stock?

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