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When the seller of a Call option hedges themselves, we know that they should buy $\Delta(t) = \mathcal{N}(d_1(t))$ amounts of the risky asset at time $t$.

But what about the riskless asset? My understanding is that they should buy $V(0) - \Delta(0)S_0$ at time $t = 0$ where $V(0)$ is the price of the option (ie the premium given by the buyer). What should they buy at time $t$?

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    $\begingroup$ The "risk free account" (so-called) is passive: initially you put $V(0)$ in, then if you need money to buy stock (because $\Delta(t)>\Delta(t-1)$) you take it out of the account, if you sell stock you put the proceeds back in (increasing your balance or reducing your debt). $\endgroup$
    – noob2
    Sep 10 '20 at 16:39
  • $\begingroup$ Thanks for the reply. When do we sell stocks though? The Gamma is always positive so we buy an increasing number of stocks is what I understand $\endgroup$
    – medihde
    Sep 10 '20 at 20:18
  • $\begingroup$ Gamma positive $\rightarrow$ we buy when price goes up, sell when price goes down. $\endgroup$
    – noob2
    Sep 10 '20 at 20:29
  • $\begingroup$ Could you expand on that please? $\endgroup$
    – medihde
    Sep 10 '20 at 22:02

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