Quant interview questions

1,322 questions · page 32 of 34

• A quadratic passes through (0,1), (1,3) and (2,7). What is its value at x = 1.5?Numerical methods · Applied
• Estimate ∫₀¹x³ dx with Simpson’s rule on two equal intervals.Numerical methods · Applied
• For a smooth function, how does the error of the midpoint rule compare with…Numerical methods · Applied
• You solve Ax = b in double precision (about 16 significant digits) and A has…Numerical methods · Applied
• Why does Gaussian elimination use partial pivoting?Numerical methods · Applied
• An explicit scheme for the advection equation uₜ+2uₓ = 0 uses Δx = 0.01.Numerical methods · Applied
• In double precision, what does 1 - math.cos(1e-8) evaluate to?Numerical methods · Applied
• Double precision can represent every integer up to 2ᵏ exactly, but not every…Numerical methods · Applied
• A loop total = 0.0; for _ in range(10): total += 0.1 leaves total == 0.9999999999999999.Numerical methods · Applied
• Stepping the heat equation, part 2 of 3Numerical methods · Applied
• Newton’s method for a square root, part 2 of 3Numerical methods · Applied
• Integrating an exponential, part 2 of 3Numerical methods · Applied
• Where doubles run out of digits, part 2 of 3Numerical methods · Applied
• Your implied-volatility solver uses pure Newton–Raphson. Which input breaks it?Numerical methods · Advanced
• You need x = A⁻¹b. Why does production code not compute the inverse?Numerical methods · Advanced
• Computing a variance as 𝔼[X²]−(𝔼[X])² sometimes returns a small negative number. Why?Numerical methods · Advanced
• What is the order of convergence of the secant method, to three decimal places?Numerical methods · Advanced
• An explicit scheme for the heat equation with unit diffusion requires Δt ≤ Δx²/2.Numerical methods · Advanced
• You sum ten million small positive numbers in float32. What goes wrong and what fixes it?Numerical methods · Advanced
• Linear interpolation of eˣ on an interval of width h = 0.1 starting at 0 has…Numerical methods · Advanced
• You interpolate a discount curve linearly in the logarithm of the discount factors.Numerical methods · Advanced
• Trapezoid estimates of ∫₀¹x² dx are 0.375 with step h and 0.34375 with step h/2.Numerical methods · Advanced
• Newton’s method for a square root, part 3 of 3Numerical methods · Advanced
• Integrating an exponential, part 3 of 3Numerical methods · Advanced
• Where doubles run out of digits, part 3 of 3Numerical methods · Advanced
• Stepping the heat equation, part 3 of 3Numerical methods · Expert
• A busy matching engine, part 1 of 3Systems and low latency · Foundation
• An L1 cache reference costs about 1 ns and a main-memory reference about 100 ns.Systems and low latency · Foundation · Free solution
• AVX-512 registers are 512 bits wide. How many float64 values does one hold?Systems and low latency · Foundation
• A cache line is 64 bytes. How many 32-bit integers fit in one?Systems and low latency · Foundation
• A single scan reads 1 GB from main memory at a sustained 20 GB/s.Systems and low latency · Foundation
• A ring buffer has capacity 1024 and wraps its index with a bit mask instead of a modulo.Systems and low latency · Foundation
• A multicast feed delivers packets with sequence numbers 1001, 1002 and then 1005.Systems and low latency · Foundation
• You sort 1,000 latency samples in ascending order.Systems and low latency · Foundation
• A timestamp counter ticks at 3 GHz. How many ticks elapse in one microsecond?Systems and low latency · Foundation
• An array-based book pre-allocates one slot per price tick.Systems and low latency · Foundation
• You join a price level behind 800 shares.Systems and low latency · Foundation
• Designing an order book, part 1 of 3Systems and low latency · Foundation
• A burst on the feed, part 1 of 4Systems and low latency · Foundation
• Walking a matrix through the cache, part 1 of 3Systems and low latency · Foundation