Consider the forward payer swap settled in advance, that is, each reset date is also a settlement date. The LIBOR Li(t) reset at Ti is used to determine the cash flow at Ti. Suppose the payments made at Ti are discounted by the factor 1/1+_αi+1L_i(T_i) so that the floating cash flow is defined to be.

while the fixed cash flow is

Here, α_i+1 is the accrual factor over (T_i,T_i+1]. Show that the time-t value of this forward payer swap is equal to that of the vanilla swap with the same fixed swap rate K.

Transcribed Image Text:

di +1 Li (Ti) 1+&i+1Li(Ti)