Basics of Quantitative Finance

Explore how random variables and probability distributions are used to model uncertainty in finance.

Learn how to calculate expected values, use linearity, and apply conditional expectation in finance.

Understand key measures of risk and dependence between financial variables.

Explore foundational theorems that justify model-based finance.

Distinguish between simple and continuously compounded returns.

Understand why asset prices are often modeled with lognormal distributions.

Learn how to discount future cash flows to present value.

See how risk-neutral pricing uses discounted expectations to value assets.

Understand the foundation of pricing theory in modern finance.

Learn how to derive the fair value of a forward or futures contract.

Use put-call parity to build synthetic positions and test for arbitrage.

Explore the logic behind pricing with risk-neutral expectations.

Understand how investors balance risk and return mathematically.

Learn how optimal portfolios lie along the efficient frontier.

Measure and model portfolio diversification using correlation.

Evaluate performance accounting for volatility.

Model asset prices as stochastic processes.

Learn the standard model for asset price evolution.

Explore why asset prices are modeled with lognormal distributions.

Use simulation to estimate prices of complex instruments.

Understand deeper assumptions in financial modeling.

Explore pitfalls when models do not generalize to reality.

Compare the impact of drift and randomness in asset evolution.