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knowing that the payoff of a ECC at maturity T is given by $C_T = max(S_T-K,0)$ can we deduce by the law of one price that $C_t = max(S_t-K,0)$ given that K is the strike price? In particular, why do make the effort and find pricing strategies for the ECC that give us arbitrage free prices if the first remark already holds?

I have the feeling that I confuse different topics, but I do not see how these are connected.

Appreciate any help!

Anton2107
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  • No it does not hold. For example we can have $S_t<K$ so that your expression is zero but the claim is still valuable since we might have $S_T>K$ at maturity. – fes Jun 15 '23 at 18:33
  • Thank you! I agree that my reasoning above is wrong but I do not get how it does not violate the law of one price: if two securities have the same market value at a future time T, they must have the same value at any other time prior to t. So why does $C_T = max(S_T-K,0)$ not imply the latter? – Anton2107 Jun 16 '23 at 13:12
  • What you call $C_t$ is not really the price of any asset. – fes Jun 16 '23 at 13:46
  • Ah so that's why it is not working. Thank you very much! – Anton2107 Jun 16 '23 at 14:18

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