IRS swap rate with floating + spread

[ThomR]

I want to calculate the swap rate for an IRS where the floating leg is LIBOR+x bp. How can I calculate the swap rate and x that make the swap worth zero at inception?

Thanks in advance!

 

[DavidS]

If you define a swap rate is the fixed rate that makes the swap worth zero at inception, you can use the same swap rate formula by replacing forwardRate with (forwardRate + spread). See more details at FinPricing - Pricing interest rate swap, pricing interest rate basis swap, pricing amortizing swap, pricing accreting swap, pricing average swap, interest rate swap valuation model

 

[vertigo]

you wouldn't calculate x to make the swap have a pv of zero at inception, it would be the fixed rate, i.e., the coupon on the fixed leg, or the forward swap rate. say i receive floating and pay fixed,

floating leg: + LIBOR + x
fixed: -k

then i will calculate k to ensure that the PV

sum_{i} P(0,t_i) (t_i-t_{i-1}) (L(t_{i-1},t_i)+x-k)

is equal to zero

x is usually the spread or the margin added onto LIBOR, it would be specified in the contract a priori to any calculation being completed.

read brigo's book on interest rate models