Part of reading 20, section 4.4 Using Options
“The PVBP of the call option is substantially less than that of the 30-year bond. We will therefore need more par value of the option than of the bond it replaces if we are to maintain the portfolio duration. To derive the needed par value of the option, we multiply the par value of the bonds we are selling by the ratio of the bond’s PVBP to the option’s PVBP: 0.2113/0.149 = 1.418. Thus, we sell 6,800 par of the 30-year bond and buy 9,640 underlying par amount of the option (approximately equal to 6,800 × 1.418). The resulting portfolio is shown in Exhibit38; with equivalent market value and duration, it has an effective money duration equal to that of the pre-trade portfolio.”
I understand we want to keep the same Effective duration as initially (7.82) and same total MV (59,720).
How is the quantity (6800) of US 30Y bonds to be sold computed?
Thanks for your help.