Quant interview questions

378 questions · page 6 of 10 · Clear filters

• An Ornstein–Uhlenbeck process has θ = 2 per year and σ = 0.4.Stochastic calculus · Applied
• A stock has expected return 10%, the risk-free rate is 3% and volatility is 25%.Stochastic calculus · Applied
• Standard Brownian motion is observed at W₄ = 2. What is 𝔼[W₁|W₄ = 2]?Stochastic calculus · Applied
• What is Var(∫₀¹Wₛ dWₛ)?Stochastic calculus · Applied
• An Ornstein–Uhlenbeck process dX = 2(1−X) dt+σ dW starts at X₀ = 5.Stochastic calculus · Applied
• What is ∫₀ᵗWₛ dWₛ?Stochastic calculus · Advanced · Free solution
• 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
• Moving from the real-world measure to the risk-neutral one, what changes about…Stochastic calculus · Advanced
• What is Var(∫₀²s dWₛ), to three decimal places?Stochastic calculus · Advanced
• What can you say about ∫₀ᵗf(s) dWₛ for a deterministic, square-integrable f?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
• 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
• You deepen your trees from depth 3 to depth 12. What happens to bias and variance?Machine learning · Foundation
• A model’s predictions at a point have bias 0.3 and variance 0.2, and the…Machine learning · Foundation
• As you train longer, training error keeps falling while validation error starts rising.Machine learning · Foundation
• A node holds 40 positive and 60 negative examples.Machine learning · Foundation
• A logistic regression has weights w = (2,−1) and bias −1.Machine learning · Foundation
• One-dimensional points 1,2,3,10,11,12 are clustered by k-means with k = 2 and…Machine learning · Foundation
• A point’s mean distance to others in its own cluster is 2, and to the nearest…Machine learning · Foundation
• A classifier has 30 true positives, 20 false positives and 10 false negatives.Machine learning · Foundation
• A classifier predicts probability 0.8 for an example that is in fact positive.Machine learning · Foundation
• How many learnable parameters does a fully connected layer from 100 inputs to…Machine learning · Foundation
• A softmax output layer receives logits (2,1,0).Machine learning · Foundation
• Why is ordinary shuffled k-fold cross-validation wrong on a financial time series?Machine learning · Applied · Free solution
• Why do gradient-boosted trees usually beat deep networks on daily…Machine learning · Applied
• You cluster assets by return correlation with k-means and the result looks arbitrary.Machine learning · Applied
• A classifier assigns scores at random. What is its expected AUC?Machine learning · Applied
• In a ten-dimensional unit cube, what fraction of the volume lies within 0.1 of some face?Machine learning · Applied
• Data are uniform in the unit hypercube in 10 dimensions.Machine learning · Applied
• A node has 50 positives and 50 negatives.Machine learning · Applied
• In gradient boosting, what happens if you halve the learning rate (shrinkage)…Machine learning · Applied
• Twenty percent of messages are spam.Machine learning · Applied
• What does the EM algorithm guarantee when fitting a Gaussian mixture model?Machine learning · Applied
• An anomaly detector has sensitivity 90% and specificity 95%.Machine learning · Applied
• You apply a strictly increasing transformation to a classifier’s scores.Machine learning · Applied
• Gradient descent on f(x) = x² starts at x = 1 with learning rate 0.1.Machine learning · Applied