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To price a call/put option with two possible future states of the world, I understand we can price the option by essentially calculating the price of a replicating portfolio that gives the same returns in either state of the world. However:

1) Why do we always consider a portfolio with the underlying asset and risk-free bonds? Could we consider other portfolios and price accordingly?

2) The model assumes the agent can borrow/lend at a risk-free rate. Is that plausible?

3) I'm assuming these are European options, is that correct?

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  • $\begingroup$ (1) Using these two assets is both necessary and sufficient in the BSM model, in other models there might be additional assets required if there are other "sources of risk" than the risk of fluctuations in the underlying asset. (2) The big banks can borrow (against collateral) at low rates that are close to SOFR or OIS rates which we can equate to $r_f$ for our purposes. (3) Yes, the BSM model assumes European exercise. $\endgroup$
    – nbbo2
    May 10, 2020 at 19:37
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    $\begingroup$ If your option is written on IBM stock, why would you trade Apple, Exxon or Pfizer stock to hedge it? $\endgroup$ May 10, 2020 at 19:41
  • $\begingroup$ @DaneelOlivaw I haven't studied finance in a formal setting and am unsure about the "hedging" part of a replication portfolio. I assumed the use of replication was merely pricing, rather than hedging. $\endgroup$
    – Student
    May 10, 2020 at 19:43
  • $\begingroup$ Hedging and Replication are more or less synonymous. If you are Long a Put Option you hedge it by replicating a Short position in the same Put option. And vice versa. $\endgroup$
    – nbbo2
    May 10, 2020 at 20:34

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