Is it correct to write 'valuable asset'?

It is not wrong.

While it is true that an asset by definition must have value, some assets have more value than others. An asset worth a million dollars is more valuable than an asset worth a hundred dollars.

In the light of that, the hundred dollar thing is just an asset, while the million dollar thing is a valuable (as in high value) asset.

Value sometimes implies 'high value' as in the town places a value on the school. In other contexts it is a mere number: a house-clearer will place a value on a shelf of paperback books (because that's his job), but it is likely to be merely nominal. Similarly with asset; the assets of a company include staplers and pencils, but if you are called an asset to the firm it is implied that you are a valuable asset. Valuable itself no longer shares this ambiguity: the meaning 'possible to put a price on' (as opposed to invaluable) is hardly used, and the almost invariable meaning these days is 'having a high value'.

There are also contexts where an asset is simply something the subject has in possession, not necessarily to their benefit. Consider an idiom toxic asset as an example. That said, unless you are working within such a context, simply calling something an asset already has positive connotations and implications of benefit and value. While it's not wrong to say valuable asset, consider if asset would be a more concise way to make your point.

It depends on the context. Say you possess a set of assets, one of which is fluency in Aramaic. In some professions this may be a valuable asset. In other professions, it may be less valuable.