Forwards and Futures on Fixed Income Securities
FP(on a fixed income security)=(S0−PVC)×(1+Rf)T
=S0×(1+Rf)T−FVC
PVC:present value of the expected coupon payments
FVC:future value of the coupon payments
The value of the forward contract prior to expiration
Vt(long position)=[St−PVCt]−[FP/{(1+Rf)^(T−t)}]
current forward price (FPt) on the same underlying and with the same maturity
Vt(long position)=[(FPt−FP)/(1+Rf)^(T–t)]
Bond futures
accrued interest(経過利息)=(days since last coupon payment/days between coupon payments)×coupon amount
full price = clean price(債券の経過利息を含まない価格) + accrued interest = clean price + AI0
FP=[(full price)(1+Rf)T−AIT−FVC]
AIT:the accrued interest at maturity of the futures contract
QFP=FP / CF
CF:コンバージョンファクター
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