You've actually stumbled upon something that is (or at least has been) a matter of debate among some History scholars (I know, I used to live with one.)
Her speciality was Islamic Law (The Principles Of Muhammadan Jurisprudence
by Rahim, Abdur was a favourite of hers) but she also dealt with European tribes and customs, and I spent many a 'happy' evening listening to her discussions on the subject. I contacted her to get her opinion on this, and this was her reply:
"Read the Alamannorum. It is all in there."
Sigh. So I did.
The Leges Alamannorum (Pactus legis Alamannorum and Lex Alamannorum) are a group of Germanic texts dating from around the 8th-12th century. They deal specifically with Wergild, and give a pretty damn complete list of crimes and rates of payment due, from grave robbing (80 shillings) to raping a free woman (40 shillings) or a servant (6 shillings).
The price for killing a free man was 200 shillings (the same as in your question, luckily!), 300 for a deacon, 600 for a priest, etc, but only 40 for a shepherd, baker, blacksmith or other servant/indentured man. Kill a slave, and you only had to replace with property worth the same value as the slave, usually another slave.
Interestingly, the price for killing a free woman was twice that of a free man, at 400 shillings. This separates the Alamanni from the Saxony and Islamic people of the time, who gave women half the value of men - Islam still does, by the way.
To give an idea of how thorough these documents can be, they include prices for striking somebody (1 shilling), striking with blood drawn (1.5s), striking with baring skullbone (3s), striking which produces skull splinter (6s), striking which exposes brain matter to the touch (12s) and striking in which brain matter is separated from the victims head (40s):
"Wenn aber aus dieser Wunde das Gehirn heraustritt, wie es geschehen mag, so daß der Arzt es mit einem Heilmittel oder einem Seidentuch verbindet, und später heilt und bewiesen wird, daß es wahr ist, büße man mit 40 Schillingen."
But when comes out of this wound the brain, as it may happen so that the doctor with a cure or with it combines a silk scarf, and later heals and it is proved that it is true to atone with 40 shillings
There are a lot of ways to wound somebody, and these documents go quite a way to list them and the various prices for wergild. As a man's physical health was his livelihood, this was quite important. Lost a toe? Have 3 shillings. Lost a foot? Have 40 shillings. Genitals? Also 40, but only 20 if you still have them, but they don't work.
It even lists prices for stealing or killing geese, ducks, crows, pigeons and cukoos.
I give these examples so you can get an idea of how detailed this document can be, and so you can understand how strange it is that it does not give a price for a dead child. A number of scholars assume that this means there was no price for a dead child, but there is some debate, due to this passage:
"Wenn ein Weib schwanger ist und durch die Tat eines andern das geborene Kind tot ist oder wenn es lebend geboren wird und nicht bis neun Nächte lebt, zahle der, dem es zur Last gelegt wird, 40 Schillinge"
If a woman [Note: not a free woman] is pregnant and by the action of another, the child born is dead or if it is born alive and not living up to nine nights, pay of which it is accused, 40 shillings
This passage clearly gives a price for the unlawful killing of an unborn child (including killed during birth or dying not long after as a result of) as 40 shillings (the same as a non-free adult), so how can a born child be worth nothing? The common argument -and I believe the only logical one- is that, once the child is born, the price was set as it would be for an adult of the same social stature.
Edited to add:
It is worth noting that the Alamannorum texts do mention children in regards to inheriting goods and other things like that, and they give different wergild values for crimes committed by children, so it's not like the authors didn't think about children and how the law changed with regards to them.
Also, older children were often the only source of income for aged parents, as there were no such thing as pension funds or retirement plans back then for most of society. Your child was your future income, and to lose a healthy one could easily be a death sentence, especially if the parents are too old to have more.
This means that, contrary to popular opinion, the value of a live, healthy child could actually be seen as greater in a society where young children are plentiful but regulary died of illness, etc. If you lose your only son, to relace him you might need to have two or three more children to have a good chance of at least one of them reaching adulthood. A healthy child living to adulthood was quite rare in comparison to today, and therefor harder to achieve. This makes the death of a healthy child a much greater financial burden on a family back then than it does now, and wergild was concerned primarily with atoning for financial loss, not emotional one.