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 6 of 8 · Clear filters
- A stock has 30% volatility, the index 15%, and their correlation is 0.6.Regression and econometrics · Foundation · Free solution
- Your errors are heteroskedastic. What is still true of the OLS coefficients?Regression and econometrics · Applied
- With orthonormal regressors, the OLS coefficient is 2 and the ridge penalty is λ = 3.Regression and econometrics · Applied
- A regression has XᵀX = [[2, 1], [1, 2]] and Xᵀy = [4, 5].Regression and econometrics · Applied
- You accidentally duplicate every row of your data set and rerun OLS.Regression and econometrics · Applied
- A spread follows an Ornstein–Uhlenbeck process dX = θ(μ−X) dt+σ dW with θ = 5 per year.Time series · Applied
- A hidden level follows a random walk with innovation variance 1 and is observed…Time series · Expert
- What is the rank of [[1, 2, 3], [4, 5, 6], [7, 8, 9]]?Linear algebra · Foundation
- What is the largest eigenvalue of [[2, 1], [1, 2]]?Linear algebra · Foundation
- You build X₂ = 0.6 Z₁+c Z₂ from independent standard normals so that X₂ is…Linear algebra · Foundation
- Can three assets be pairwise correlated at −0.5?Linear algebra · Applied · Free solution
- Geometrically, what does ordinary least squares compute?Linear algebra · Applied
- A 10 × 10 correlation matrix has a largest eigenvalue of 6.Linear algebra · Applied
- With A = [[2, 1], [1, 3]] and x = (1,2)ᵀ, what is the first component of ∇ₓ(xᵀAx)?Linear algebra · Applied
- A matrix has eigenvalues 1, 2 and 3. What is the trace of A²?Linear algebra · Applied
- A two-state Markov chain has transition matrix [[0.9, 0.1], [0.5, 0.5]] (rows sum to one).Linear algebra · Applied
- Assets A and B correlate at 0.9, and B and C at 0.9.Linear algebra · Advanced
- Two assets have volatilities 20% and 10% and correlation 0.5.Linear algebra · Advanced
- For standard Brownian motion, what is 𝔼[W₃W₇]?Stochastic calculus · Foundation
- For standard Brownian motion, what is Var(W₁+W₂)?Stochastic calculus · Foundation
- What is the correlation between W₁ and W₄ for standard Brownian motion?Stochastic calculus · Foundation
- What is the quadratic variation of Xₜ = 0.3 Wₜ over [0,2]?Stochastic calculus · Foundation
- A stock follows geometric Brownian motion with drift 8% and volatility 20%.Stochastic calculus · Foundation
- A stock at $100 follows GBM with drift 10% and volatility 20%.Stochastic calculus · Foundation
- What is d(Wₜ²)?Stochastic calculus · Applied · Free solution
- For standard Brownian motion, what is 𝔼[W₄⁴] – the fourth moment at time 4?Stochastic calculus · Applied
- A Brownian motion with drift 0.5 per unit time starts at zero.Stochastic calculus · Applied
- What is 𝔼[e^(0.4W₂)], to four decimal places?Stochastic calculus · Applied
- A spread follows an Ornstein and Uhlenbeck process with reversion speed θ = 0.5 per year.Stochastic calculus · Applied
- A stock has expected return 10%, the risk-free rate is 3% and volatility is 25%.Stochastic calculus · Applied
- For standard Brownian motion, what is Pr(W₂ > W₁ > 0)?Stochastic calculus · Applied
- Standard Brownian motion is observed at W₄ = 2. What is 𝔼[W₁|W₄ = 2]?Stochastic calculus · Applied
- What is 𝔼|Wₜ| at time t = π/2?Stochastic calculus · Applied
- Standard Brownian motion starts at 0. What is the probability it hits +1 before −2?Stochastic calculus · Applied
- Standard Brownian motion starts at 0 and stops on hitting +1 or −2.Stochastic calculus · Applied
- What is 𝔼[∫₀²Wₛ² ds]?Stochastic calculus · Applied
- What is Var(∫₀¹Wₛ dWₛ)?Stochastic calculus · Applied
- Using the Itô product rule on tWₜ, which identity holds?Stochastic calculus · Applied
- A stock follows GBM with drift 10% and volatility 20%.Stochastic calculus · Applied
- An Ornstein–Uhlenbeck process dX = 2(1−X) dt+σ dW starts at X₀ = 5.Stochastic calculus · Applied