SIG interview questions

A basic mental-maths screen that tests whether a candidate separates probability from payoff.

You pay $3 to play a game. A fair six-sided die is rolled: you receive $12 on a 6 and nothing otherwise. Should you play once? What would change if you could play 1,000 independent times?

A basic prop-trading exercise tests whether candidates translate probabilities into a price and a trading decision.

A contract pays $100 if a coin lands heads and $0 if it lands tails. You believe heads has a 55% probability. What is the fair value? Would you buy at $54, and would you sell at $56?

Fermi estimation is a standard prop trading round. You have sixty seconds.

How many tennis balls fit in a Boeing 747? You have one minute.

A prop-trading technical round checks whether you can construct a hedge from payoffs rather than memorise Greeks.

A stock is $100 today. Tomorrow it will be either $120 or $90. A call with a $100 strike pays $20 in the up state and $0 in the down state. How many shares hedge one short call in this one-period…

A sizing follow-up tests whether you distinguish an estimated edge from a known probability.

A trade wins 55% of the time and loses 45% of the time. It makes or loses 1% of the capital allocated. What is full Kelly sizing, and why might a trading desk use less?

The interactive trading game used at every prop firm.

I have a bag with 10 balls, each numbered 1 to 10. I draw three and the contract settles on their sum. Make me a market. Then I show you that one of the balls drawn is a 10, what's your new market?

Options market making interviews probe what you do when you cannot hedge continuously.

You're short gamma into the close, with earnings after the bell. What are your options, and what do you do?

Tests whether you reason about why a bet is being offered, not just its expected value.

I offer you a bet: I roll a fair die, and if it comes up 6 I pay you $10; otherwise you pay me $1. Do you take it? How much would you pay for the right to play 100 times?

Trading interviews use this to test whether you can construct an arbitrage on the spot.

State put-call parity. A stock trades at $100. The $100 strike call trades at $8, the put at $5, and the risk-free rate is 4% with 1 year to expiry, no dividends. Is there an arbitrage? If so,…

Standard for derivatives desks and quant trading interviews.

Name the inputs to the Black-Scholes model and the direction each moves a call option's price. Which input is not observable, and what does that imply?

Market-making interviews will push hard on gamma.

Define delta and gamma. You are short a straddle and delta-hedged. Explain what happens to your position as the underlying moves, and what you're actually long or short.

Volatility desks ask this after the skew question.

Implied volatility differs across expiries as well as strikes. What does an upward-sloping vol term structure mean, and what does it mean when it inverts?

Volatility desks ask this to see whether you understand the market, not the model.

Equity index options show higher implied volatility for downside strikes than upside. Explain why the skew exists and what it tells you about the market's assumptions.

Asked to see whether you can explain a counterintuitive result clearly under pressure.

Three doors: one hides a car, two hide goats. You pick door 1. The host. Who knows what's behind each door. Opens door 3 revealing a goat, then offers you the chance to switch to door 2. Should you…

A classic Bayesian warm-up at quant trading firms.

You have two coins. One is fair; the other lands heads 75% of the time. You pick one at random and flip it 3 times, getting heads every time. What is the probability you picked the biased coin?

The signature exercise at proprietary trading firms.

Make me a market on the sum of the digits of a randomly chosen phone number in the room. Then I'll trade against you. Explain how you'd think through the whole exercise.