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Converting US Treasury CMT to Discount Yields

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?

Quantitative Finance Asked by MikeRand on December 13, 2020

1 Answers

One Answer

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 $FaceValue*CashflowatMaturity/(1+CMTRate/2)^{2*YearFrac365}$

Answered by dm63 on December 13, 2020

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