- #1
rwinston
- 36
- 0
Hi
I have a question about rearranging the following equation (I saw this in a finance book):
If we rearrange and differentiate
[tex]
Z(t;T) = e^{-\int_{t}^{\tau}r(\tau)d\tau}
[/tex]
We get
[tex]
r(T) = -\frac{\partial}{\partial{T}}(\log{Z(t;T)})
[/tex]
My question is: how do we differentiate the exp(-int()) portion? How can we simplify the integral as an exponent?
Thanks!
I have a question about rearranging the following equation (I saw this in a finance book):
If we rearrange and differentiate
[tex]
Z(t;T) = e^{-\int_{t}^{\tau}r(\tau)d\tau}
[/tex]
We get
[tex]
r(T) = -\frac{\partial}{\partial{T}}(\log{Z(t;T)})
[/tex]
My question is: how do we differentiate the exp(-int()) portion? How can we simplify the integral as an exponent?
Thanks!