“Also, higher dividends will lower the number of bonds to short sell for calls and lower the number of bonds to buy for puts.”
It is the last sentence on page 358 on the book 5. I do not understand why higher dividends will lower the number of bonds to buy for puts.
Dividend increases (γ increases) will lead d1 to decrease (d1=ln(S/X)+(r−γ+σ2/2)T/σT‾‾√ ). d1 decreases will lead d2 decreases (d2 = d1 – σT‾‾√). As d2 decreases, N(–d2) will increase. N(–d2) increases will lead the number of units of bonds bought to increase (p = e–rTXN(–d2) – Se–γTN(–d1), since N(–d2) is the the number of bonds to buy for puts). So, higher dividends will higher the number of bonds to buy for puts, rather than lower.
Is that correct?