In response to the title: "How to respond to an HTTP OPTIONS request?" To answer that, I'd want to know why you want to respond to an OPTIONS request? Who/what is sending you an OPTIONS request, and why? Many public servers respond with some form of "error" or "not allowed" (500, 501, 405). So, unless you're in a specific situation where your clients will be reasonably sending OPTIONS requests and expecting useful/meaningful information back (e.g., WebDAV, CORS), you probably want to respond with: "don't do that."
In terms of your question about the "OPTIONS /conversion HTTP/1.1" request: unless you know that there's some client of your server, a client which would send an OPTIONS request to "/conversion" and expect a response with "Allow: CONVERT," the answer is no: it wouldn't make sense to respond like that. I think that most implementations that do support OPTIONS and respond with "Allow," respond with standard HTTP methods.
Here's a great article on the topic.
Summary: OPTIONS is immediately problematic because it doesn't support caching. Alternatives: server-wide metadata: try well-known URI's. Resource-specific: try using a Link header on its responses, or a link in the representation format for that resource.
Lastly, if what you're after is a service description, have a look at WADL or RSDL.
EDIT:
dotnetguy makes a good point in the comment below: OPTIONS is undeniably valuable in certain contexts (e.g., CORS); I certainly didn't mean to suggest otherwise.