[Quantlib-users] Using instantaneous forward rates

[Arkadiy N. <ark...@gm...>]

Have a question for the community, which is a bit on obscure side. When using piecewise yield curve with interpolation on forward rates, how should I use instantaneous forward rates to make sure the original instruments (those set up by ratehelpers) are priced accurately?

Here is what I mean:

suppose all I have is two deposit helpers for 1M and 3M and I chose linear interpolation.
Instantaneous forward rates (which span 0.001 fraction of a year) are flat prior to 1M. If these were daily rates, I would be looking for the rate that satisfies exp(-rate/365)^31 = 1M DF (1M DF is implied by 1M deposit rate). How do I modify this for the instantaneous forward? Is it exp(-rate*0.001)^85 (this is approximate - .001 is about 2.74 times smaller than 1 day of 365-day year)

And then to get the rates filled out between 1M and 3M, is it 
PRODUCT (exp(-(1M_NodeRate + k*n) *0.001)) = 3M DF ?

Where k is the slope (it is linear interpolation after all) and n is the number of times 0.001 fits between 1M and 3M

Which would mean I can calculate k analytically

Thank you in advance! I am going to go ahead and test my theory out anyway, but if it’s incorrect, I need the advice anyway!

Sent from my iPhone