The Japanese stock market has announced it will be open on Monday.
I am sure you know that there is not just one market where the yen trades, so if you shut one market you would just be hurting investors who don’t have the ability to also trade on other markets. In other words, local individual investors may not be able to trade (and may therefore be locked into losing positions), while large multinational corporations would basically have no problem. That is actually a big concern, because foreign currency trading is currently enjoying a boom in Japan, so a fair number of individuals are engaged in such trading.
Also, shutting the markets would very possibly create a greater feeling of panic, and would certainly cause distortions. Markets and investors like to know (set) the price of things, and if you close a market, it cannot do that, and people get nervous.
The only time you would want to close a specific market is if it’s facilities or systems cannot function properly, or perhaps if there is a major panic underway. For example, after 9-11 the U.S. stock markets were closed for a day or two or three, but that was primarily because the NYSE was near the affected area. People would have had difficulty moving about the city, and may have been concerned for their safety, and even in ourning. Since Japan’s market is in Tokyo and not in Sendai, it can function, and there is no reason to expect a panic when it is time to open on Monday. If Tokyo was directly hit by a major earthquake, then the Tokyo market might close.
Besides, the stock markets in Asia and Europe are not really in any significant amount of turmoil (down 1%, but that is not outraqeous), and the last I heard, the yen was trading higher. If you got the idea that world markets are in turmoil from something like CNN, well, they just want to make things sound dramatic and exciting.
Also, don’t forget that the markets are important tools, and limiting the use of such important tools would seem to be unhelpful in a time of crisis. For example, one of the reasons given why the yen is trading higher is because Japanese companies are repatriating foreign cash because they want to have yen on hand for whatever reason to help deal with the earthquake. Not having that capability to repatriate yen could very well hamper recovery efforts.
If all of this sounds like I am cold and calculating, I apologize. I am only addressing your question, not the human aspect of the earthquake. Like many here, I have family and friends in Japan, so as soon as I heard about how large the earthquake and tsunami was, I was on the phone to ascertain their safety (and thankfully, everyone was fine).