**Key topics to Study for Quantitative Trading Interviews **

**1. Basic Probability Concepts **– Sample spaces, events, and outcomes.

– Probability axioms (Kolmogorov axioms).

– Conditional probability and independence.

– Law of total probability and Bayes’ theorem.

**2. Random Variables **– Discrete and continuous random variables.

– Probability mass functions (PMFs) and probability density functions (PDFs).

– Cumulative distribution functions (CDFs).

– Expected value (mean) and variance of random variables.

**3. Distributions **– Common discrete distributions (e.g., Bernoulli, Binomial, Poisson).

– Common continuous distributions (e.g., Uniform, Normal, Exponential).

– Properties and characteristics of these distributions.

**4. Joint Distributions **– Joint PMFs and joint PDFs.

– Covariance and correlation.

– Conditional distributions and conditional expectations.

**5. Transformations of Random Variables **– Sum and difference of random variables.

– Scaling and linear combinations.

– Moment-generating functions (MGFs) and characteristic functions.

**6. Limit Theorems **– Law of Large Numbers (LLN).

– Central Limit Theorem (CLT).

– Weak law of large numbers.

**7. Time Series Models **– Basics of time series and stochastic processes.

– Autoregressive (AR) and moving average (MA) models.

– Stationarity and ergodicity.

– Autocorrelation and partial autocorrelation functions.

– GARCH, ARCH and EWMA models for volatility forecasting.

**8. Monte Carlo Methods **– Monte Carlo simulation for pricing and risk assessment.

– Variance reduction techniques (e.g., control variates, antithetic variates).

**9. Markov Chains **– Transition matrices and Markov property.

– State space, absorbing states, and recurrent states.

– Steady-state and long-term behavior of Markov chains.

**10. Option Pricing Models **– Black-Scholes-Merton model for European options.

– Greeks (Delta, Gamma, Vega, etc.).

– Exotic options and pricing methods.

**11. Risk Management **– Value at Risk (VaR) and Conditional Value at Risk (CVaR).

– Risk measures and portfolio risk assessment.

These topics are fundamental for quantitative trading, as they help you understand the probabilistic nature of financial markets and enable you to build and analyze trading strategies.