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The put-call parity equation: $$c-p = S_0 - Ke^{-rT}$$ can be seen as a equality in cash flows--namely, buying a call and selling a put have equivalent cash flows to the underlying stock price less the strike price of the options. Taking this into $t=0$ means the current price of the call less the current price of the put must equal the present value of the ...


I think this is where your logic goes wrong: $(C_t − P_t − S_t)e^{r(T−t)} + K$ With reference to the above equation, you are saying that "...To that money that we owe, we add the money that we owe to the contract buyer.." Yes, $(C_t − P_t − S_t)e^{ r(T−t)}$ is the money that we owe, but $K$ is not referring to money that we also owe the contract buyer. ...

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