I would say that volatility relates more to price action rather than volume.
If you think about it, price action is really a result of volume being pushed around i.e. the dominant force between buyers and sellers at any give time frame dictate the price action. Therefore Volatility is really created by the underlying Volume and Liquidity.
Let me define Volume and Liquidity based on my own idea/experience, and not the dictionary meaning:
Volume: The Amount of Money (filled or unfilled) at various price points close to At The Money.
Liquidity: The rate (per second, or per minute depending on the market you're trading) at which orders get filled. The faster the orders get filled the better the liquidity.
Example:
Let's say Yahoo is currently trading at around $20
There are Buy limit orders @ 19.5 for $50,000, @ 19 for 85,000, @ 18.5 for 95,000
There are Sell limit orders @ 20 for $60,000, @ 20.5 for 75,000, @ 21 for 85,000
So there's great volume at various points At The Money, but after 10 minutes the scenario looks only $1,000 is filled at points between 19.5 and 20.5
This illustrates that despite good volume there's poor liquidity. i.e. there's big money waiting to be filled on either side of the current price but very little is actually filled during the elapsed time period.
On the other hand:
Let's say Yahoo is currently trading at around $20
There are Buy limit orders @ 19.5 for $5,000, @ 19 for 8,000, @ 18.5 for 9,000
There are Sell limit orders @ 20 for $6,000, @ 20.5 for 7,000, @ 21 for 8,000
In this case, the Volume isn't that great as the previous scenario, but in the next 10 minutes all the orders between 18.5 and 21.5 have been filled and the price stands again at $20.
This illustrates great Liquidity despite lower Volume, because money is being filled at a great speed. Traders can enter and exit positions in the market very quickly at or near current price.
I'm not trying to oppose your view new_trader but just providing my own view. Peace!