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Extrapolate (bootstrap) CDS spread curve (term structure)

Hi everybody i need your help to extrapolate (bootstrap) CDS spread curve.
In fact, as input data i only have spread 1,3,5,7,10 Y and i have already computed a tool allowing to calculate the spread for each month maturity during 1 to 10 Y.
I'm now looking for a way to extrapolate the curve, i mean i would like to calculate spread from 10 to 30 years and even spread from 0 to 1 under the assumption that default intensity is constant between two dates.
For interpolation i have used the folowing equation where PD is the default probability, S the Survival, tk the interpolation date, si the spread for the ieme counterparty.

\( PD_{i,tk}=1-exp(-\frac{s_{i,tk}.t_{k}}{LGD_i}) \)
\( S_{i,tk}=1-PD_{i,tk} \)
\( \tau_{n} < tk < \tau_{n+1} \)
\( S_{i,tk} = S_{i,\tau_{n}}. (\frac{S_{\tau_{n+1} }}{\tau_{n}}) ^{(\frac{ tk -\tau_{n}}{\tau_{n+1}-\tau_{n}})} \)

If you have an idea