# Continuously compunded forward rate

• Jul 31st 2012, 02:07 AM
Continuously compunded forward rate
$e^{R(t,S,T)(T-S)}=\frac{B(t,S)}{B(t,T)}$

Is R(t,S,T) a constant discount rate or just a discount rate.

And why ?

Thanks
• Jul 31st 2012, 11:37 AM
Wilmer
Re: Continuously compunded forward rate

$A cpd continuosly at r% for t years: A[e^(rt)] I assume you're aware of that? • Jul 31st 2012, 11:54 AM ebaines Re: Continuously compunded forward rate Quote: Originally Posted by Wilmer$A cpd continuosly at r% for t years: A[e^(rt)]

I assume you're aware of that?

Note that 'r in that equation is a constant. If the OP is asking about compounding where the rate varies over time this formula doesn't apply.

Also a nit to pick, to avoid any confusion - the 'r 'is not a percent, but rather a rate expressed as a decimal. Thus if the interest rate is 10% /year then 'r' would be 0.1 in the formula.
• Jul 31st 2012, 12:21 PM
Wilmer
Re: Continuously compunded forward rate
Good point...however, I'm fairly sure the OP will "get the point"; if not:

\$2340 @ 3.1% cpd. continuously for 3 years:
2340[2.7183....^(.031 * 3)] = ~2568.06

Try same with daily cpd. instead: you'll get 2568.04; so don't get taken in
by the SOUNDS of cpd. continuously !(Cool)
• Aug 19th 2012, 04:07 AM