If there is one then lots of Japanese designers is ignoring them.

from what I know, basically it's cap Y with the first cross stroke touching the arm.

but since I didn't go to school in japan I am not 100% sure (95% maybe)

The yen symbol was invented overseas by Western journalists who needed a symbol to use in financial articles. At the time, typewriters were the main writing tool in use, so something that could easily be typed — a Y followed by a backspace and a hyphen or equal sign — became the convention. Thus, there is no official description of ¥ any more than there is an official description for $ or @ or &.

In Japan itself, the ¥ is not used terribly often, being essentially a Latin typographic symbol; and it does not appear on currency. Instead, the ideogram 円 is used. This character also means "circle" and has the same origin as the character for the Chinese yuan.

Incidentally, "dollar" can be written 弗 in Japanese, a rather clever innovation since it is otherwise rarely used and resembles a dollar sign.