PRACTICE GUIDE SIG
SIG Stochastic Processes Practice Test
Susquehanna (SIG) does not publish the shape of its stochastic processes screen, and candidates describe it as 10 to 15 questions in 30 to 60 minutes, roughly two to five minutes per question, answered by picking one of the options.
Those are ranges across firms running this format rather than Susquehanna (SIG)'s own figures, so treat them as the shape to train against and check the instruction screen on the day for the marking rule.
Outcry is not affiliated with Susquehanna (SIG) and has no access to their assessment content. This guide describes an assessment format that candidates report publicly; the questions here are generated by Outcry and are not Susquehanna (SIG)’s own.
What it screens
A global quantitative trading firm famous for teaching decision-making through poker.
- ✓Martingale arguments and optional stopping applied to games
- ✓Gambler's ruin: absorption probabilities and expected duration
- ✓Recognising when a process is a martingale (and when the argument breaks)
- ✓Random-walk intuition: recurrence, drift, and scaling
Where it sits at Susquehanna (SIG)
A global quantitative trading firm famous for teaching decision-making through poker. What that means for the screen is that the questions tend to be drawn from the work rather than from a textbook, so the format below is the shape to train against rather than a syllabus.
Candidates also report 4 other screens at Susquehanna (SIG), covered separately on this site. Where a firm runs several, they usually sit in one round rather than spread across the process, so the pacing of the whole set matters more than any single section.
The format
Susquehanna (SIG) does not publish this screen's shape, and it varies between firms, so these are the ranges candidates report rather than exact figures.
| Questions | 10 to 15 |
|---|---|
| Time | 30 to 60 minutes |
| Per question | two to five minutes |
| Negative marking | No |
| Answer style | Multiple choice or short typed answer |
| Where it sits | Research-track screen, before the technical interviews |
What it tests, with a worked example
Every example below is generated by Outcry, drawn from the same question generators the timed drills run. None of them is Susquehanna (SIG)’s.
Markov chains
Transition matrices, absorbing states, and expected time to absorption.
Example
Regime Prob Mean Variance Calm 0.6 2 1 Stressed 0.4 4 25
Daily P&L runs in one of two regimes, drawn fresh each day from the table above. What is the variance of the daily P&L?
- 14.6
- 10.6
- 11.56
- 30
Answer 11.56
Law of total variance. The within-regime part is E[Var(P | regime)] = 0.6×1 + 0.4×25 = 10.6. The regime means differ by 2, so the between-regime part is Var(E[P | regime]) = p(1−p)(Δmean)² = 0.6×0.4×4 = 0.96. Total = 10.6 + 0.96 = 11.56. Averaging the two variances and stopping there drops the 0.96 that comes from the regimes sitting at different levels.
Random walks and martingales
Stopping times, the optional stopping theorem, and gambler's ruin.
Example
Fills arrive at a mean of 12 per hour. Each fill is 2 lots or 4 lots with equal probability, independent of how many fills arrive. What is the expected total lots in an hour?
Answer 36
Condition on the number of fills N. Each fill averages (2 + 4)/2 = 3 lots, so E[lots | N = n] = 3n. The tower rule takes the expectation of that: E[lots] = 3 × E[N] = 3 × 12 = 36.
Inference and research integrity
What a result means, and what it would take for it to mean nothing.
Example
A Monte Carlo estimate uses 900 paths. Roughly how many are needed to halve the standard error?
- 3600
- 1800
- 14400
- 450
Answer 3600
Standard error scales as 1/√n, so cutting it in half needs four times the paths: 3600.
Stating assumptions
Research screens mark the assumption you named as much as the number you produced.
Conditional expectation
Tower property and the expectation of a stopped process, which is most of what these rounds ask.
Example
Two venues fill orders as independent Poisson processes, 5 and 3 per minute. Each fill is front-month with probability 0.5, independently of everything else. What is the arrival rate of front-month fills per minute?
- 8
- 4
- 2.5
- 2
Answer 4
Superposition: two independent Poisson streams merge into one Poisson stream at 5 + 3 = 8 per minute. Thinning by an independent coin keeps it Poisson, at 8 × 0.5 = 4 per minute. The rates add - they are not averaged, and the quiet venue does not drop out.
Overfitting and multiple testing
Why a result at the five per cent level means very little after the twentieth test.
Example
Residuals from a daily regression have first-order autocorrelation 0.6. What is the approximate Durbin-Watson statistic?
- 0.8
- 3.2
- 0.6
- 1.4
Answer 0.8
DW ≈ 2(1 − ρ̂) = 2 × (1 − (0.6)) = 0.8. Two means no autocorrelation, below two means positive autocorrelation and above two means negative. At 0.6 the residuals repeat themselves, so the effective sample is smaller than the observation count suggests, the standard errors come out wrong, and a backtest's t-statistics cannot be read at face value.
What a good score looks like
Research screens are marked by a person more often than a machine, so a numeric cutoff is rarely visible. Candidates consistently report that a wrong answer with a stated assumption scores better than a right answer with none.
How to train for it
- 01Rebuild the standard results rather than memorising them - a two-state chain, gambler's ruin, the regression slope from correlation and standard deviations.
- 02Say what would falsify the result. Research screens are looking for the person who reaches for that first, and it is the cheapest habit to build.
- 03Get comfortable with conditional expectation specifically. More of these rounds reduce to the tower property than to anything else.
TRAIN IT HERE
The drills that match each section
Martingale Mutiny
Optional stopping played as a game. Try to find a betting strategy that beats a fair coin.
Ruin Walker
Gambler's ruin with live absorption probabilities.
Distribution Lab
Recognise a distribution from how its samples behave.
SIT THE FULL BATTERY
All the sections back to back on one clock, marked the way the real screen marks them, with a by-skill breakdown at the end. Included with any pass.
Also reported at Susquehanna (SIG)
Common questions
- Is the SIG stochastic processes test multiple choice?
- Reported as multiple choice or short typed answer. Formats move, so treat this as the shape rather than a guarantee.
- How long is the SIG stochastic processes test?
- Candidates report 10 to 15 questions in 30 to 60 minutes, roughly two to five minutes per question.
- Is there negative marking on the SIG stochastic processes test?
- No. A wrong answer costs nothing beyond the mark you would have earned, so leaving an item blank is never better than guessing at it.
- How do I practise for it free?
- Every drill linked on this page is free to play, with no account, inside a daily run cap. Questions are generated fresh each run, so there is nothing to memorise between attempts.