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For a European Call option, by proposing the initial price of the underlying asset I am sure to be able to meet my commitments, however this result is not true for a Put option. However, by proposing the strike as a the initial price then I meet my commitments. I would like to know if there is more general results concerning this ? I found nothing by myself on the internet except some stuff that exceeds my mathematical level (in continuous time).

Thanks!

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    $\begingroup$ I am not sure what you are asking. I think what you are saying is that $c \le S_0$ and $p \le K$. It is true and well known. Many books on options have a first chapter called "bounds on option prices" or similar title that discusses these and other bounds.. You can google this title. See for example www3.cs.stonybrook.edu/~skiena/691/lectures/lecture7.pdf on Page 7. $\endgroup$
    – nbbo2
    Jun 23, 2022 at 12:44
  • $\begingroup$ Thank you, what I wanted to ask is if there exists more general result about price that insures the seller to meet his commitments which are interesting ? For example, what I have in mind is that for a European call option, the price $S_0$ is a super replication price but is it the smallest price that ensures the seller meets its commitments ? Because if it is not the case, we can do nothing with this notion since it is no interesting for the buyer no ? $\endgroup$
    – coboy
    Jun 23, 2022 at 14:45

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