Braces around both sides of cases (with text)

Here, I replace the cases environment with a \left\{\!\begin{aligned}...\end{aligned}\right\}. The \! seems necessary to overcome a small space introduced, I think by the leading &.

\documentclass[12pt]{article}
\usepackage{amsmath}
\usepackage{amssymb}
\begin{document}
\begin{equation*}
\hat{C}(\hat{S},1) = \frac{1}{E} C(S,T) =
\left\{\!\begin{aligned}
&0 &\text{ if } S<E,\\[1ex]
&\frac{S}{2E} &\text{ if } S=E,\\[1ex]
&\frac{S}{E} &\text{ if } S>E.
\end{aligned}\right\}
\end{equation*}
\end{document}

If one wanted to preserve the \textstyle of the cases environment,

\documentclass[12pt]{article}
\usepackage{amsmath}
\usepackage{amssymb}
\begin{document}
\begin{equation*}
\hat{C}(\hat{S},1) = \frac{1}{E} C(S,T) =
\left\{\!\begin{aligned}
&0 &\text{ if } S<E,\\[1ex]
&\textstyle\frac{S}{2E} &\text{ if } S=E,\\[1ex]
&\textstyle\frac{S}{E} &\text{ if } S>E.
\end{aligned}\right\}
\end{equation*}
\end{document}

You can simply use the (d)rcases environment from mathtools.

Also, I think it's better to use \widehat with capital letters.

\documentclass[12pt]{article}
\usepackage{mathtools}
\usepackage{amssymb}

\begin{document}

\begin{equation*}
  \widehat{C}(\widehat{S},1) = \frac{1}{E} C(S,T) =
  \begin{rcases}
    \begin{dcases}
      0 & \text{ if } S<E, \\
      \frac{S}{2E} & \text{ if } S=E, \\
      \frac{S}{E} & \text{ if } S>E.
    \end{dcases}
  \end{rcases}
\end{equation*}

\end{document} 

You can exploit the \newcases feature in mathtools:

\documentclass[12pt]{article}
\usepackage{amsmath,mathtools}
\usepackage{amssymb}

\makeatletter
\newcases{lrdcases}
  {\quad}
  {$\m@th\displaystyle{##}$\hfil}
  {$\m@th\displaystyle{##}$\hfil}
  {\lbrace}
  {\rbrace}
\newcases{lrdcases*}
  {\quad}
  {$\m@th\displaystyle{##}$\hfil}
  {{##}\hfil}
  {\lbrace}
  {\rbrace}
\makeatother


\begin{document}

\begin{equation*}
\hat{C}(\hat{S},1) = \frac{1}{E} C(S,T) =
\begin{lrdcases}
0            &\text{if $S<E$,}\\[1ex]
\frac{S}{2E} &\text{if $S=E$,}\\[1ex]
\frac{S}{E}  &\text{if $S>E$.}
\end{lrdcases}
\end{equation*}

\begin{equation*}
\hat{C}(\hat{S},1) = \frac{1}{E} C(S,T) =
\begin{lrdcases*}
0            & if $S<E$,\\[1ex]
\frac{S}{2E} & if $S=E$,\\[1ex]
\frac{S}{E}  & if $S>E$.
\end{lrdcases*}
\end{equation*}

\end{document}

According to the conventions of mathtools, the *-variant has the second column typeset in text mode.

However, I'd use the left brace only.