### Value of irregular floating coupon

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**November 6th, 2018, 2:51 pm**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?

Problem

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.

Question

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?

Problem

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.

Question

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?