Bond futures formula

CFA Level II Derivatives
#1

Hi everyone,

The formula for futures price of a bond is: [(full price) * (1 + r)^T - Accrued Interest at Maturity - Future Value of Coupons]

Where:

Full price = Clean price + Accrued Interest

Accrued Interest = Days since last coupon payment / Days between coupon payment * Coupon amount

Question

Fo the futures price formula, is there a double counting of coupons? We counted it as part of Future Value of Coupons so why the need to further deduct Accrued Interest at Maturity (which is based on coupons)?

Basically, I can’t understand why there has to be a deduction of Accrued Interest at Maturity.

Thank you for your time.

#2

When you buy the bond you pay the Accrued Interest hence its an addition to the price.

When you sell the bond you receive the Accrued Interest hence its a deduction from the price.

#3

Since the Accrued Interest arises from Coupon payments. Would it be right to say that should I buy the bond at coupon payment date, then there would be no Accrued Interest and accordingly no Accrued Interest at Maturity?

Thanks for taking the time to reply.

#4

Yes, I think that is correct. However I have a qns: If Let say I buy coupon on Feb, semi- annual coupon. The last coupon is Jan, the next coupon is in June. My future contract expire in Sept. The AI(0) will be from Jan-Feb, then which one is the AI(T)? Jan to June or Jan to Sept? and I will have to minus the FV of the next coupon in June-Sept?

#5

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