There are lots of open source options analysis code libraries, but there is a dearth of options analysis software that have graphical user interfaces (GUI). It seems that those with enough sophistication to demand options analysis are either knowledgeable enough to program computers themselves, or have sufficient resources to obtain ready-made solutions (e.g. from their broker). It could also be because those who know enough about options are using their time to make money instead of giving away software for free. I have only found a few options analysis software.
A derivatives calculator that includes many pricing models. Useful for exploring options pricing.
This seems to be the only such open source tool of its kind. It is no longer maintained, but it could serve as inspiration for your own options analysis tool should you choose to build one in the future.
This is the options analysis tool that accompanies the book Options, Futures, and Other Derivatives by John D. Hull. It is freely available on the author's website. It's not exactly open source, but since the tool essentially consists of several Microsoft Excel files, you will be able to tweak it around for your own needs. An older version of DerivaGem (version 2.01), had Excel as well as the equivalent OpenOffice files. Recent versions (such as version 4.00) only have Excel files. You should be able to find the older versions through the Internet Archive's Wayback Machine.