Quant interview questions
1,322 questions in the style trading and research firms ask, from probability and brainteasers to options, statistics and coding. Every question is open to read; the 50 in the free sample show their worked solutions here.
282 questions · page 7 of 8 · Clear filters
- A stock with 20% volatility has real-world drift 10%; the risk-free rate is 2%.Stochastic calculus · Applied
- In Sₜ = S₀e^((μ−σ²/2)t+σWₜ), what is the −σ²/2 doing?Stochastic calculus · Advanced
- Which of these is a martingale?Stochastic calculus · Advanced
- What is Var(∫₀²s dWₛ), to three decimal places?Stochastic calculus · Advanced
- A Brownian motion is conditioned to return to zero at time 4.Stochastic calculus · Advanced
- For a standard Brownian motion, what is Pr(max _(t ≤ 4)Wₜ ≥ 2), to four decimal places?Stochastic calculus · Advanced
- What can you say about ∫₀ᵗf(s) dWₛ for a deterministic, square-integrable f?Stochastic calculus · Advanced
- A stock at $100 follows a driftless geometric Brownian motion with 30% volatility.Stochastic calculus · Advanced
- Xₜ = 0.5t+Wₜ starts at 0. What is the probability it hits +1 before −1, to three decimals?Stochastic calculus · Advanced
- A driftless Brownian motion starts at 0.Stochastic calculus · Advanced
- The area under a Brownian path, I = ∫₀³Wₛ ds, has mean zero. What is its variance?Stochastic calculus · Advanced
- In the CIR model dr = κ(θ−r) dt+σ√r dW with θ = 0.04 and σ = 0.3, what is the…Stochastic calculus · Advanced
- Under ℙ, W is standard Brownian motion.Stochastic calculus · Advanced
- What does the Feynman–Kac theorem connect?Stochastic calculus · Advanced
- Why price a bond option under the forward measure rather than the risk-neutral one?Stochastic calculus · Expert
- A node holds 40 positive and 60 negative examples. What is its Gini impurity?Machine learning · Foundation
- In a ten-dimensional unit cube, what fraction of the volume lies within 0.1 of some face?Machine learning · Applied
- A support vector machine has |w|= 4. What is the width of its margin?Machine learning · Applied
- Gradient descent with momentum uses a learning rate of 0.01 and β = 0.9.Machine learning · Applied
- A batch normalisation layer follows a fully connected layer of 128 units.Machine learning · Applied
- A classifier flags 500 cases, of which 40 are true positives, and misses 60 positives.Machine learning · Applied
- Data are uniform in the unit hypercube in 10 dimensions.Machine learning · Applied
- An anomaly detector has sensitivity 90% and specificity 95%.Machine learning · Applied
- What does the kernel trick actually buy you?Machine learning · Advanced
- You increase the batch size from 32 to 512 without changing anything else. What happens?Machine learning · Advanced
- Why did rectified linear units largely replace sigmoids in deep networks?Machine learning · Advanced
- You cluster a universe of assets from their correlation matrix.Machine learning · Advanced
- A signal has an information coefficient of 0.05 against returns, both approximately normal.Alpha and signal research · Advanced
- What does the probability of backtest overfitting measure?Alpha and signal research · Expert
- Treatment A succeeds in 81/87 small cases and 192/263 large ones; treatment B…Research case studies · Advanced
- What is the expected number of fair coin flips to see two heads in a row?Data structures and algorithms · Applied
- What does the recurrence T(n) = 4T(n/2)+Θ(n²) solve to?Data structures and algorithms · Applied
- You insert 1,000 keys into a hash table with 1,000 buckets using a uniform hash.Data structures and algorithms · Applied
- How many structurally different binary search trees can hold the keys 1,2,3,4,5?Data structures and algorithms · Applied
- What is the largest sum of a contiguous subarray of [−2,1,−3,4,−1,2,1,−5,4]?Data structures and algorithms · Applied
- What is the length of the longest strictly increasing subsequence of…Data structures and algorithms · Applied
- Items have weights 1,3,4,5 and values 1,4,5,7.Data structures and algorithms · Applied
- You roll a fair six-sided die up to three times, stopping whenever you like and…Data structures and algorithms · Advanced
- With both union by rank and path compression, what is the amortised cost of a…Data structures and algorithms · Advanced
- Any comparison sort must, in the worst case, make at least ⌈log₂n!⌉ comparisons.Data structures and algorithms · Advanced