"Individual Craftsmanship"...I am not sure how you want to apply this skill set later. Craftsman to me means someone who simply applies a tool set, it does not imply (according to the dictionary definition) whether professionally to earn money or in order to teach or treat it as a personal hobby. So please let me comment on all three:
Professionally in the financial industry:
While academic achievements can greatly help to get the foot in the door, it could not matter less whether you got a PhD or finished high school in the day-to-day business. I have seen excellent traders who were made MD when they were 25-26 years old. True wizards in the craft of generating excellent risk-adjusted returns rather than just people swinging for the fences. If you have an inclination to high level math and want to get into modeling and pricing exotic derivatives I would rather hire a kid who learned it all by himself than a mid 30s who had to go through his BS, MS, and PhD math program to achieve the same level. I think most on the street would concur with this opinion. As long as you got the tools and skills how you acquired such skills does not matter in the slightest. I often times come across extremely "academically arrogant" people who interview for a job. Most always arrogance masks other weaknesses and I prefer to spend the time during the interview to dig deeper into such weaknesses than having to listen to rehearsed derivations of Black-Scholes or the HW model. Having said that, given you are looking to acquire a quant finance skill set, and you finish your MS I would probably need to know of what quality your MS program was. To give you an example: If you did the MSCF program at Carnegie Mellon I would consider that as a stamp of approval (not because of the school name but just because the program is excellent) to sit you at a derivatives desk given all your other credentials match up. A generalized MS program where you have done very little to no programming, stochastic calculus and derivatives pricing would make me much more cautious. So it depends again what you actually know not the school you went to. If you believe your MS cannot land you at a tier one investment bank (regardless of where you actually want to work) then I would consider applying for a top PhD program given you have a passion for a particular subject matter that you could imagine spending 2-3 years on intensively researching.
Teaching:
Well, simple, go straight for the PhD program. Not much else to say.
Hobby:
If you believe a PhD program gives you more (maybe because of available resources, grants, professors, peers) than just learning on your own then go for the PhD program. Otherwise there are endless ways to further your skill set in quant finance, you could pick up/improve your C++ skill set and writing pricers or applicable algorithms yourself which you could potentially monetize later.
Hope this helped. Sorry I can speak most about the professional track because I worked for 13 years in this field and also underwent an MS program (wont comment on the specific one but it was a door opener plus really pushed me to the limits and actually beyond in what I ever imagined I was capable of doing). I enjoy practicing my skills and being measured competitively vs other traders by the PnL I generate rather than trying to impress others with geek talk.
