I don’t know theoretically accurate solution to the following problem that I frequently face valuing irregular floating rate notes. Can somebody help me out?
Let’s assume that there is a market of zero-coupon risk-free bonds.
Price of a bond at time t with maturity at T and face=1 is P(t,T).
Bond’s interest rate is R(t,T) = (1/P(t,T)-1)/(T-t).
Forward interest rate from T_1 to T_2 at t is F(t,T_1,T_2) = (P(t,T_1)/P(t,T_2) – 1)/(T_2 – T_1).
There is a tradable derivative “f” that pays R(T_1, T_2) (interest rate R fixed at T_1) at T_3>T_2.
What is value of “f” at t=0?
The question is trivial for the case T_3=T_2: f(0) = P(0,T_2)*F(0,T_1,T_2) – “discounted forward rate”. Is it possible to find f(0) for T_3>T_2?