Developer for Tree Probability Model

We are seeking for senior developer for Tree Probability Model
1. Calculate probability tree of small moves normalized by volatility
- N steps, T=N*dt, T_small = dt or T/N
- u==probaility of going up
- 1-u==probability of going down
- amount of jump is Vol prediction on larger timescale T
- jump per small interval is volpred/sqrt(T/T_small)
- Number of iterations of this generates a set of trajectories/paths

2. Calculate the number of paths that touch less than value for terminal value as the ratio of total measured path
- Be able to calc the delta probability between two points both in terminal value
- And in never touched value. ie. this is the number of trajectories as a ratio of all tested trajectories that stayed within this upper and lower range.

3. Allow for time of day dependant vol predictions and probabilities...
- TOD can be expressed as a unit of N
4. To bypass this all. (mod the time dependence predictions)
- Is there an analytic solution, for the simplest case.
We prefer to work with individual developers