How do I know if I am ready to apply for a PhD (In terms of the dissertation topic)?

In terms of the dissertation topic and not the readiness for the level of studies, how do I know if I am ready to apply for a PhD?

Facts about moi:

1/4 I am currently a masteral student of mathematical finance, expecting to graduate sometime this year. I'm not particularly interested in mathematical finance anymore unless it's in a rigorous context (more info here). I am still interested in taking a PhD as I was when I started master's but want a different focus, namely in Stochastic (fancy word for Random) Analysis, a branch of mathematics used in mathematical finance and physics.

2/4 My background in Stochastic Analysis comprises of

1) 2 3-unit courses with no research projects, but some problem sets 2) Probability Theory with no research project, but some problem sets 3) Few applications of it in some of our Finance classes

3/4 Stochastic Analysis is mainly used in the Q part of mathematical finance while my thesis is on the P part, concerned mainly with statistics and credit risk modelling.

4/4 With this, I feel I have no background in research of not only stochastic analysis but also mathematics.