# OIS Floating Leg Value at Swap Start with OIS discounting with payment lag

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.

• 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.
– Attack68
Jan 29 '21 at 21:34
• 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? Jan 29 '21 at 22:04