Do I need a second master's or can i already apply for a PhD?

Pardon the dumb question if ever. I notice similar questions all sound like "can I get a second master's?" but mine is "do I need?"

I am nearly finished with my master in mathematical finance. I have finished my thesis and have one course left to take.

Edit: I am about to graduate from a third world university and am planning to apply for a PhD in a first world university.

I am interested in taking up a PhD in a different branch of mathematics called stochastic analysis (stochastic calculus. or whatever it's called.) but am wondering if my background is insufficient. If so, I may take up a second master's.

Given my limited background in stochastic analysis and other information (below), can I already apply for a PhD with stochastic analysis for my dissertation topic, or might I need a second master's first?

Some information:

1. 
   

   I am not particularly interested in mathematical finance anymore unless it is in a rigorous context rather than with computers, modeling, statistics, non-mathematical finance, simulations, etc. As of right now, I no longer have any plans to go into industry.

   
   


2. 
   

   My background in Stochastic Analysis is 2 courses on Stochastic Calculus, 1 prerequisite course for Stochastic Calculus (probability) and 2 halves of classes which apply the stochastic calculus.

   
   


3. 
   

   I don't know about the basics of one kind of stochastic calculus as we were taught mainly the other kind.

   
   


4. 
   

   My thesis is about credit risk, having mainly to do with statistics, the part of mathematical finance I don't want to go in to, if I were still interested in mathematical finance. Hence, I feel have no background in mathematical research given that the research conducted was mainly to do with statistics and finance.

   
   

I have read a sample PhD proposal and have no clue what to put for methodology. I am not quite sure what kind of research methods pure mathematicians have.

Furthermore, while I technically passed the thesis, I scored the lowest passing mark.