### Value of floating coupon with payment delay

Posted:

**November 13th, 2018, 2:27 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”)

Actually, I asked this question on another forum and got the following answer from bearish:

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”)

Actually, I asked this question on another forum and got the following answer from bearish:

So, now I am curious what models do people usually use and how exactly they calculate the adjustment?As long as T_3 is different from T_2 you need a model to calculate what is usually (if somewhat sloppily) referred to as the convexity adjustment. This adjustment would be applied to the zero volatility value of P(0,T_3)*F(0,T_1,T_2).

You might have received a quicker response if posting in the Student forum.