convert discount rate to continously compounded yield to maturity

[mouna]

HI
I'm a Ph D in finance. My research is about interest rate term structure modeling. My database is the united states yield curve. For the estimation of the short term interest rate process, I use the 3 month treasury bill rate from the FRED SITE WEB. This rate is a discount rate. I want to convert it to continuously compounded yield to maturity.

I have read in an article that :

for bond equivalent yields (BEY) the formula is: r (YTM)= 1/M* In (1+r(BEY)*M/100)

for discount rate r(D) the formulas is : r (YTM)= -1/M* In (1-r(D)*M/100)

please can you help me and tell me if these formulas are correct.

thanks

Mouna

 

[quotes]

Suppose you have a bill with discount rate 4% and 1 month to maturity.
The actual discount factor is 4%/12. So the bond is worth 1-4%/12 =PV
Another point of view on this bond is
(100/PV)=(1+YTM)^(1/12)
Then you may solve the YTM.
I guess the formula is Not correct.