# No-Arbitrage Futures Price (Derivatives)

With the following data (Question 1 in practice problem of Curriculum), why dont they include Accrued interest at futures contract expiration in the first pricing formula, but do include it in the adjusted price formula.

Exhibit 1. Current Data for Futures and Underlying Bond

Futures Contract:

Quoted futures price: 125.00

Conversion factor: 0.90

Time remaining to contract expiration: Three months

Accrued interest over life of futures contract: 0.00

Underlying Bond

Quoted bond price 112.00

Accrued interest since last coupon payment: 0.08

Accrued interest at futures contract expiration: 0.20

The no-arbitrage futures price is equal to the following:

F0(T) = FV0,T(T)[B0(T + Y) + AI0 – PVCI0,T]

F0(T) = (1 + 0.003)0.25(112.00 + 0.08 – 0)

F0(T) = (1 + 0.003)0.25(112.08) = 112.1640

The adjusted price of the futures contract is equal to the conversion factor multiplied by the quoted futures price, adding the accrued interest of 0.20 in three months to get a total price of 112.70.

F0(T) = CF(T)QF0(T)

F0(T) = (0.90)(125) = 112.50

I would have solved the problem a little differently.