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I'd like to convert the US Treasury Constant Maturity series (par, semi-annual coupon, Actual/365 daycount convention) into Discount Factors (for appropriate comparison for certain money-market series, calculation of forward rates, conversion to alternative daycounts, etc.).

The "hypothetical security" reflecting the CMT quote is straightforward for 6 months to 30 years: $PV=FaceValue$ that pays $FaceValue * CMT Rate/2$ every 6 months before maturity, $FaceValue*(1+CMTRate/2)$ at maturity (even on weekends/holidays, since it's an interpolated curve).

What is the hypothetical security for the 1, 2, and 3 month CMT quotes? Is it a discount bond (and, if so, what's the discount formula to arrive at $PV$)? Or is it a coupon bond with $PV=FaceValue$ that pays $FaceValue*(1+CMTRate * YearFrac365)$ at maturity?

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I think it is a coupon bond with semiannual coupons of $CMTRate$, thus a payment of $FaceValue*(1+CMTRate/2)$ at maturity and no other payments due. The $PV$ of this bond is $FaceValue*CashflowatMaturity/(1+CMTRate/2)^{2*YearFrac365}$

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  • $\begingroup$ Interesting. So you'd "overpay" the coupon on 1-month and 3-month bills (by taking 0.5 years of simple interest) and let PV adjust upward from face value accordingly? I guess that makes the PV a dirty price on these quotes (having accrued 3-5 months of interest)? $\endgroup$ – MikeRand Sep 5 '20 at 14:35

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