Is it safe/OK/acceptable to assume that $PV_{float}=1$ at on a Swap that projects and discount with the same OIS index, at starting date, if payments are done with a 2D lag i.e. $t_{pay} = t_{endCoupon}+2D$. This is for bootstrapping context.

  • $\begingroup$ well technically I would go would no. A floating leg that depends on an OIS fixing between t_0 and t_1, but is paid on t_3, is different to a floating leg that depends on a the ois fixing between t_0 and t_1 and pays t_1. $\endgroup$
    – Attack68
    Jan 29 '21 at 21:34
  • $\begingroup$ So, with this I should not use $VP_{float}=VP_{fixed}$ -> $1 = r_{fix}\sum_{i=1}^{N-1}\tau_{t_{start,i},t_{end,i}}DF_{t_{pay,i}} + \left( 1 + r_{fix}\tau_{t_{start,N}, t_{end,N}}\right)DF_{t_{pay,N}}$ for a IRS OIS discounting bootstrap right? $\endgroup$ Jan 29 '21 at 22:04

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