Basics of Quantitative Finance
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This course covers everything from expectations and variance to portfolio optimization and stochastic models. You'll learn how asset prices evolve, how to apply no-arbitrage pricing, and how to evaluate portfolio performance using risk-adjusted metrics. Designed as a technical starting point for aspiring quants, this course balances theory and practice with clean, intuitive explanations.
Random Variables and DistributionsExplore how random variables and probability distributions are used to model uncertainty in finance.Expectation, Linearity, and Conditional ExpectationLearn how to calculate expected values, use linearity, and apply conditional expectation in finance.Variance, Covariance, and CorrelationUnderstand key measures of risk and dependence between financial variables.Law of Large Numbers and Central Limit TheoremExplore foundational theorems that justify model-based finance.
Arithmetic vs Log Returns1 questionDistinguish between simple and continuously compounded returns.Lognormal Returns and Compounding1 questionUnderstand why asset prices are often modeled with lognormal distributions.Time Value of Money and Discount Factors1 questionLearn how to discount future cash flows to present value.Real-World vs Risk-Neutral ExpectationSee how risk-neutral pricing uses discounted expectations to value assets.
Law of One Price and ReplicationUnderstand the foundation of pricing theory in modern finance.Forward and Futures PricingLearn how to derive the fair value of a forward or futures contract.Put-Call Parity and Synthetic Positions1 questionUse put-call parity to build synthetic positions and test for arbitrage.Risk-Neutral Valuation Intuition1 questionExplore the logic behind pricing with risk-neutral expectations.
Mean-Variance Optimization1 questionUnderstand how investors balance risk and return mathematically.Efficient Frontier and Capital Market LineLearn how optimal portfolios lie along the efficient frontier.Diversification and Correlation Matrix1 questionMeasure and model portfolio diversification using correlation.Sharpe Ratio and Risk-Adjusted Metrics1 questionEvaluate performance accounting for volatility.
Random Walks and Brownian MotionModel asset prices as stochastic processes.Ito Process and Geometric Brownian MotionLearn the standard model for asset price evolution.Lognormal Asset ModelingExplore why asset prices are modeled with lognormal distributions.Monte Carlo Simulation and Application to PricingUse simulation to estimate prices of complex instruments.
Stationarity, Ergodicity, and Path DependenceUnderstand deeper assumptions in financial modeling.Overfitting, Misspecification, and Model RiskExplore pitfalls when models do not generalize to reality.The Role of Drift vs Volatility in MarketsCompare the impact of drift and randomness in asset evolution.
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