Quantitative Finance

Understanding present and future value concepts, compounding, discounted cash flows, and the relationship between interest rates and valuation.

Basics of probability, random variables, distributions, expected value, variance, conditional probability, and Bayes' Theorem in finance.

Key distributions (normal, lognormal, binomial, Poisson, fat-tailed) and their applications in financial modeling and risk management.

Descriptive statistics, estimation concepts, Central Limit Theorem, hypothesis testing, and confidence intervals for financial data.

Vectors, matrices, linear equations, and matrix decompositions with applications to portfolio analysis and factor models.

Derivatives, marginal effects, multivariable calculus, constrained optimization, and convexity in portfolio optimization.

Integrals, continuous compounding, differential equations, and foundations for continuous-time finance models.

Setting up programming environments, basic syntax, data structures, and implementing financial calculations programmatically.

Importing and managing financial datasets, organizing time series data, and creating effective visualizations.

Root-finding algorithms, interpolation techniques, and numerical integration for solving financial problems.

Stock ownership, market structure, trading mechanics, equity returns, and fundamental market concepts.

Bond types, cash flows, pricing by discounting, yield to maturity, and day-count conventions.

Yield curves, zero rates, spot rates, forward rates, and bootstrapping techniques.

Duration, convexity, interest rate risk measurement, and immunization strategies for bond portfolios.

Forward and futures contracts, contract specifications, margin requirements, and market mechanics.

Commodity market structure, contango and backwardation, convenience yield, and hedging physical commodities.

Cost-of-carry pricing, arbitrage relationships, and basic hedging strategies using futures contracts.

FX market structure, exchange rate quotes, interest rate parity, and currency forwards for hedging.

Call and put options, payoff structures, moneyness, put-call parity, and fundamental option concepts.

Spreads, straddles, strangles, covered calls, protective puts, and constructing complex payoff profiles.

Swap structure, fixed-floating exchanges, notional principal, and applications in interest rate management.

Valuing swaps as bond portfolios, swap curves, and practical uses in hedging and synthetic asset creation.

CDS structure, credit risk protection, spread pricing, default probabilities, and recovery rates.

Asset securitization, CDO structures, tranching, credit risk distribution, and valuation challenges.

Convertible bonds as hybrid instruments, conversion features, valuation approaches, and other hybrid securities.

Empirical features of returns: heavy tails, skewness, volatility clustering, and implications for modeling.

Random walks, Brownian motion, Wiener processes, and Geometric Brownian Motion for stock prices.

Stochastic differential equations, Itô's Lemma, and changing variables in stochastic processes.

Fundamental theorem of asset pricing, risk-neutral probabilities, and arbitrage-free pricing frameworks.

Deriving the Black-Scholes PDE through dynamic hedging, assumptions, and implications.

Closed-form solutions for European calls and puts, formula components, and basic Greeks introduction.

Delta, Gamma, Theta, Vega, Rho: measuring and managing option portfolio risk sensitivities.

Computing implied volatility, volatility surfaces, smile patterns, and market implications.

Discrete-time lattice models, backward induction, American options, and convergence to Black-Scholes.

Simulating price paths, valuing path-dependent options, Monte Carlo error, and convergence.

Antithetic variates, control variates, stratified sampling for improving simulation efficiency.

Explicit, implicit, and Crank-Nicolson schemes for solving the Black-Scholes PDE numerically.

Asian options, barrier options, lookbacks, digitals, compound options, and their pricing approaches.

Vasicek, Cox-Ingersoll-Ross models: modeling rate evolution with mean reversion.

Heath-Jarrow-Morton framework, Libor Market Model, and calibration to market data.

Caps, floors, swaptions, and pricing interest rate options using various models.

AR, MA, ARMA, ARIMA models for stationary and non-stationary financial time series.

ARCH, GARCH models for time-varying volatility, volatility clustering, and forecasting.

OLS regression, factor exposures, hypothesis testing, and addressing time-series regression issues.

Dimension reduction, identifying principal components in yield curves and equity returns.

Fitting models to market data, optimization techniques, overfitting concerns, and model stability.

Markowitz framework, efficient frontier, diversification benefits, and portfolio optimization.

CAPM equilibrium, market portfolio, Security Market Line, beta, alpha, and model limitations.

APT framework, multi-factor models, Fama-French factors, and factor risk premia.

Sharpe ratio, information ratio, maximum drawdown, benchmarking, and risk-adjusted returns.

Brinson attribution, factor-based attribution, separating alpha from beta exposures.

Black-Litterman model, robust optimization, risk parity, and practical constraints.

Market, credit, liquidity, operational, model risk; regulatory standards and risk management objectives.

Value-at-Risk calculation methods, Expected Shortfall, stress testing, and scenario analysis.

Probability of Default, Loss Given Default, Exposure at Default, and expected loss calculations.

Structural models (Merton), reduced-form models, credit scoring, and portfolio credit risk.

Counterparty default risk, Credit Valuation Adjustment, exposure profiles, and CVA hedging.

Market and funding liquidity risk, operational risk, model risk, and qualitative assessments.

Risk limits, hedging strategies, CRO role, risk committees, and firm-wide risk culture.

Alpha generation concepts, strategy categories, development workflow, and backtesting importance.

Mean reversion concepts, pairs trading, statistical arbitrage portfolios, and regime risks.

Time-series and cross-sectional momentum, CTA strategies, behavioral sources, and reversal risks.

Value, growth, size, quality factors; constructing factor portfolios and long/short hedge funds.

Trading volatility as an asset class, delta-hedged strategies, dispersion trading, and vol risks.

Automated market making, bid-ask spread capture, inventory risk, and adverse selection.

HFT strategies, cross-market arbitrage, technology infrastructure, and competitive dynamics.

Supervised and unsupervised learning, feature engineering, model validation, and overfitting prevention.

ML for signal generation, sentiment analysis, alternative data, reinforcement learning applications.

Non-traditional data sources, natural language processing, sentiment extraction, and compliance.

Crypto market structure, unique characteristics, quantitative strategies in crypto, and specific risks.

Merger arbitrage, earnings trading, fixed income arbitrage, and event-specific risk management.

Proper backtesting methodology, avoiding biases, performance metrics, and out-of-sample testing.

Commission, spreads, slippage, market impact modeling, and incorporating costs in strategy design.

Order books, limit vs market orders, order priority, execution mechanics, and dark pools.

TWAP, VWAP, implementation shortfall algorithms, Almgren-Chriss framework, and adaptive execution.

System components, data feeds, execution systems, latency considerations, and robustness testing.

Research workflow, version control, paper trading, production deployment, and continuous monitoring.

Kelly Criterion, risk budgeting, capital allocation, leverage limits, and position sizing principles.

Market manipulation, regulatory compliance, algorithmic safeguards, and ethical responsibilities.

End-to-end strategy development: from idea generation through backtesting to deployment readiness.