It doesn't seem possible. Even though it displays correctly in the preview area, only the code appears on the submitted answer.

I have tried the following (found in the Share > Embed section of a Youtube video):

<iframe width="420" height="315" src="http://www.youtube.com/embed/nh95_KwSPVg" frameborder="0" allowfullscreen></iframe>

and

<object width="420" height="315"><param name="movie" value="http://www.youtube.com/v/nh95_KwSPVg?hl=en_US&amp;version=3"></param><param name="allowFullScreen" value="true"></param><param name="allowscriptaccess" value="always"></param><embed src="http://www.youtube.com/v/nh95_KwSPVg?hl=en_US&amp;version=3" type="application/x-shockwave-flash" width="420" height="315" allowscriptaccess="always" allowfullscreen="true"></embed></object>

Apparently, a specific AskBot module needs to be installed as explained here: https://github.com/ASKBOT/askbot-devel/blob/master/askbot/doc/source/optional-modules.rst#embedding-video

Finally found an html snippet that works great! 

Just copy and paste the html snippet below where you want by going to  Customize ----> html editor then paste where you want and change the YouTube Video number zpOULjyy-n8 with yours. You get his by going to the YouTube Video and then below the video select the share link and get the bold video number using example below:

src="//www.youtube.com/embed/zpOULjyy-n8

                        <h3>

                         Responsive 16:9 YouTube

                        </h3>
                        <div class="embed-responsive embed-responsive-16by9">
                            <iframe class="embed-responsive-item" src="//www.youtube.com/embed/zpOULjyy-n8?rel=0"></iframe>
                        </div>

I think that this could be a really useful feature and help increase the quality of answers.

According to the FAQ, at a certain level of karma one can:

• 30 insert text link, upload files
• 50 insert clickable link, answer own question immediately

Therefore I would say that inserting a video should go somewhere around here, perhaps also at 50, as it is 'interactive' like a clickable link.

If of course it is possible on this platform.

Yes, it is possible and very easy.
Just go to the youtube video, click on the "Share" link below the video, select the "embed" section, and copy/paste the code in your answer.

Example:

<iframe width="420" height="315" src="http://www.youtube.com/embed/nh95_KwSPVg" frameborder="0" allowfullscreen></iframe>

Hello, sorry but how can you access to the source code for a particular blog post ?

I do not see any "ShowSource" button on the Odoo backend under the Knwloedge Menu.