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I am reading "Volatility Trading" by Euan Sinclair. In the derivation of BSM process in Chapter 1, formula 1.2 confused me.

This is the scriptshot

It means that the value change of a hedged call position (1 Call $C_t$ and $\Delta$ short stocks).

The last term from author denotes the interest income, which is from the financing to build the position for the hedged option.

However, in my understanding, to build a position of a hedged call, you borrow money of $C(S_t)$ to buy the Call option, then short Delta stocks and lending the proceedings of $\Delta S_t$ which makes you receive $r(\Delta S_t-C)$ interest income instead of $r(C-\Delta S_t)$.

Any one can explain me which one should be correct?

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Your understanding is correct, this has been corrected in the second edition on Page 3:

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    $\begingroup$ I am a bit at a loss as to the downvote, is my answer incorrect? I am happy to retract the answer if this is the case. $\endgroup$ Apr 30, 2023 at 23:34

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