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Can someone please help me with this? I need to do a regression in order to estimate the alpha's in this following equation, but I can't seem to get this equation to be in a format that i could use regression with.Ii was just looking to simplify this equation so that I can get something in the form of Y = constant + alpha0 * something + alpha1 * something .. etc so that the regression coefficients will be my alphas.

Any advice would be greatly appreciated, thanks a lot! D(T) stands for the balance at time T, and R(T) stands for the interest rate at time T.

D(T) = D(0) * exp[alpha0 * T + alpha 1 * T^2 / 2 + Alpha 3 * (R(T) - R(0))] * ((1 / df(T)) ^ Alpha3

where df(T) = exp(summation from i to N of - R(TI) * dTI) (so df(T) is basically a constant number)

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  • $\begingroup$ Actually I think the ending part of the equation ((1+df(t))^alpha3 is not part of the exp() part of the equation. Does that make sense? Would there then be a way of simplifying for regression? Thanks a lot! $\endgroup$
    – alex
    Dec 22, 2011 at 0:07
  • $\begingroup$ alex, I've merged your two accounts, but you we'll need to register once for all to get system-wide notifications, be able to comment, update your question, etc. $\endgroup$
    – chl
    Dec 22, 2011 at 0:13

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I am assuming that the "Alpha 3" inside the exp[...] part of your formula should be an "Alpha 2", as otherwise you are missing an "Alpha 2" and have two "Alpha 3"s.

Just take the logs of both sides; simplest to divide both sides by D(0) first:

$\log (D_t/D_0) = \alpha_0T + \alpha_1 T^2/2 + \alpha_2 (R_t-R_0) + \alpha_3\log(1/df_t)$

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