First of all, you're missing a matching \right delimiter to one of your \left delimiters.
Also, you cannot break \left and \right across lines inside align (or any math environment for that matter). You need to do this manually by using a fake opposing delimiter and introducing the necessary false heights to obtain equivalent delimiters. However, an easier alternative would be to use non-matching "big" operators:

\documentclass{article}
\usepackage{amsmath}% http://ctan.org/pkg/amsmath
\begin{document}
\begin{align}
\rlap{$C(t,xxx,\tau,N,X)$}\hspace{2em} & \nonumber \\
&= N\Phi\sum_{i=1}^{n}
\Bigg[-(1+X_{\tau_{i}})P(t,T_{i})
\Bigg(\frac{\ln\frac{P(t,T_{i-1})}{(1+X_{\tau_{i}}P(t,T_{i})}}{\Sigma(t,T_{i-1},T_{i})}-\frac{1}{2}\Sigma(t,T_{i-1},T_{i})\Bigg)\\
&\phantom{{}={}} {}+P(t,T_{i-1})\Bigg[
\Bigg(\frac{\ln\frac{P(t,T_{i-1})}{(1+X_{\tau_{i}})P(t,T_{i})}}{\Sigma(t,T_{i-1},T_{i})}-\frac{1}{2}\Sigma(t,T_{i-1},T_{i})\Bigg)\Bigg]\Bigg]
\end{align}
\end{document}
The use of \hspace in the first line is to make the equation fit within the text block width. Also note the use of \phantom{{}={}} to obtain the correct spacing for the second numbered equation.