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Math Help - Continuously compunded forward rate

  1. #1
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    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
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  2. #2
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    Re: Continuously compunded forward rate

    Don't understand your question...

    $A cpd continuosly at r% for t years: A[e^(rt)]

    I assume you're aware of that?
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  3. #3
    Super Member ebaines's Avatar
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    Re: Continuously compunded forward rate

    Quote Originally Posted by Wilmer View Post
    $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.
    Last edited by ebaines; July 31st 2012 at 12:51 PM.
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  4. #4
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    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 !
    Last edited by Wilmer; July 31st 2012 at 12:33 PM.
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  5. #5
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    Re: Continuously compunded forward rate

    Thanks for your help but why is R constant?
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  6. #6
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    Re: Continuously compunded forward rate

    I'll let E Baines answer that....because I don't see WHY you're asking...
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