# Derivatives

HI guys, this is the question from the official qbank, I am having a hard time understanding it.

Currently Sheroda is long a US Treasury futures position. Parisi notes the following information for the cheapest to deliver US Treasury bond for the contract; the bond has a face value of \$100,000, pays a 7% semiannual coupon, and matures in 15 years. The bond is priced at \$156,000, has no accrued interest, and a yield of 2.5%. The futures contract expires in 8 months, and the annualized risk-free rate is 1.5%. There are multiple deliverable bonds, and the conversion factor for this bond is 1.098.

SOLUTION;

B is correct. The futures price is calculated as follows:

There is no accrued interest, but the bond pays a \$3,500 coupon in 6 months, and the future value of the coupon at expiration will be \$3,508.6958 = 3500(1.015)(2/12)

f0(T)=[\$156,000(1.015)(8/12)−\$3,508.6958] / 1.098=\$140,298.20

BUT where did 2 mon of AI for the PMT being paid after the contract maturity disappear?

MY SOLUTION :

{ [156000 - 3500/(1.015(6/12))] * 1.015(8/12) } - AI(3500 * (2/12)) / 1.098

{[FV (Spot price + AI - PV Coupon )] - AI } / conversion factor

Why they didnt use that AI in the formula?

When you buy a bond you’ll get the next coupon payment, so you have to pay for accrued interest.

When you buy (i.e., take the long position in) a bond futures contract, you don’t receive coupon payments, so you don’t have to pay for accrued interest.

i dont get it Derivatives Valuation EOC 1st question

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 0.2 SOLUTION:

1. 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

WHY DONT WE SUBTRACT ACCRUED INTEREST OF 0.2?

1. The adjusted price of the futures contract is equal to the conversion factor multiplied by the quoted futures price: F0(T) = CF(T)QF0(T) F0(T) = (0.90)(125) = 112.50 OK, I GET THIS.

2. Adding the accrued interest of 0.20 in three months (futures contract expiration) to the adjusted price of the futures contract gives a total price of 112.70.

I DONT GET THIS, WHY?

according to Mark Meldrum

F(T) = ( Spot Price + AI since last payment )* (1+r)^(t/T) - AI at futures expriration

QF(quoted futures price) = F(T) / CF

*bump