Quantitative trading internships: roles, preparation and a worked probability case

Solve the decision before reaching for a simulation

Here is an original fictional exercise, not an employer interview question. A ticket pays the number shown on one fair six-sided die, in dollars. It costs $3, plus a $0.60 transaction fee. You may buy one ticket or decline, and there are no other payments.

The expected payout is (1 + 2 + 3 + 4 + 5 + 6) ÷ 6 = $3.50. Subtract the full $3.60 cost: expected net payoff is −$0.10. A student who compares only the ticket price with the average payout would incorrectly report a $0.50 expected gain.

Declining is better on expected dollars under these assumptions. That does not mean buying always loses: rolling a six produces $2.40 net, while rolling a one loses $2.60. Distinguish an unfavorable average from a guaranteed outcome.

Now change the information, not the arithmetic rules

Suppose the die has already been rolled and you receive truthful information that the result is even. The same $3 ticket and $0.60 fee remain available after that information arrives. The possible results are now 2, 4 and 6, each equally likely.

Expected payout becomes (2 + 4 + 6) ÷ 3 = $4. Expected net payoff is $4 − $3 − $0.60 = $0.40. The answer changes because the information set changed. In a real decision, you would need to establish whether that information is reliable and whether the quoted price remains available; those are explicit assumptions here.

For practice, vary the fee or the reliability of the message and explain where your decision changes. Write the reasoning first. A small simulation can check it, but a favorable result from a handful of trials is not a replacement for the calculation.

• State which information is available before buying, and which arrives only afterward.
• Show both the expected result and at least one losing outcome.
• Explain what would make you decline even after the favorable message, such as a fee above the remaining expected edge.

Turn your preparation into an answer you can defend

For your own project, keep a one-page note containing the rules, calculation, changed assumption and resulting decision. In an interview, explain the mistake you caught rather than just showing the final number. For example: 'I initially ignored the fee. Including it reversed the decision, so I made the full cost an explicit input.' Use that wording only for work you actually did.

Choose further practice to match the role: probability and decision explanations for trading, experiment design for research, and software correctness or performance for engineering. None of these exercises establishes a particular firm's assessment format.

Before choosing between offers, ask whether you would work mainly on trading decisions, research or infrastructure. 'Who reviews an intern's reasoning when an idea does not work?' is more informative than asking whether the internship is challenging.

Before you apply

Eligibility

Jane Street welcomes applicants without a finance background. Read the specific trading role for its technical and academic expectations.

Timing

Jane Street describes typical internships of 10–12 weeks; Citadel Securities describes 11 weeks. Those durations are not application deadlines.

Location

Jane Street lists New York, London and Hong Kong internship locations. Select the office attached to the actual role.

Pay

Use the role's stated pay unit and paid weeks. Keep housing and one-time payments separate from recurring wages.

Sources: Jane Street internships · Citadel Securities internships

Job titles to search

Quantitative trading intern

Analyze information and make or support pricing, execution and risk decisions.

Trading research intern

Test evidence that could improve a trading decision or strategy.

Quantitative developer intern

Build the software used for research and trading; this is a different preparation emphasis.

Where to look

Search routes, not confirmed vacancies.

Compare the work and try an example

Use a role comparison or worked exercise to choose your preparation before tailoring an application.

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