Two Sigma interview preparation

Technology-led investment firm applying data science, machine learning, and systematic research to uncover value and innovate in financial services.

• Pricing a Simple Coupon Bond
• Brownian Motion: Compute E[W_s W_t]
• Chi-Square Test for Independence: Compute the Statistic
• Confidence Interval Width Scaling with Sample Size
• Ito Isometry: Var(∫ W_t dW_t)
• Macaulay Duration of a 2-Year Coupon Bond
• Martingale Property: E[W_t | F_s]
• Multiple Regression: Interpreting a Partial Effect
• Parametric 95% One-Day VaR (Normal Returns)
• Quadratic Variation of Brownian Motion
• Risk-Neutral Drift for a Non-Dividend Stock
• Sample Size for a Desired Margin of Error (Proportion)
• Type I/II Errors: Compute Test Power
• Black–Scholes PDE Form
• Bond Price Sensitivity Using Duration and Convexity
• CLT Bounds: Berry–Esseen Sample Size
• Compound Interest Calculation
• Ito’s Lemma: Drift of log(S_t) under GBM
• LLN Rate: Chebyshev Sample Size Requirement
• MLE for a Poisson Rate Parameter
• Multicollinearity Effects in Regression
• Regression Diagnostics: Test for Heteroskedasticity
• Risk-Neutral Drift with Continuous Dividend Yield
• Sufficient Statistic for Exponential Rate
• Time Series Stationarity: AR(1) Condition
• Two-Asset Portfolio VaR with Correlation
• Bayesian Inference with Unreliable Witnesses
• Daily Bloomberg Terminal Keystrokes
• Daily Canceled HFT Orders
• Global Daily Text Messages
• Hours of Video Uploaded to YouTube Daily
• Linear Interpolation on 2D Points
• R-Squared Symmetry: Regressing Y on X vs X on Y
• Valid Range of Common Correlation for Three Random Variables
• Explicit Solution to GBM
• Feynman–Kac: PDE to Expectation
• Girsanov: Brownian Motion under Measure Change
• MGF of an Exponential Random Variable
• Ornstein–Uhlenbeck Process: Mean Function
• Ten Prisoners Hat Puzzle - Parity Strategy
• Quant Fund GPU Backtesting Hours