This lecture is an introduction to counterparty credit risk, featuring credit valuation as well as the broad economic objectives of a financial institution. It also concludes the course.

Lecture 26: Introduction to Counterparty Credit Risk

This is a guest lecture on quanto credit hedging, including using mathematical models in trading.

Lecture 23: Quanto Credit Hedging

This guest lecture features the Ross Recovery Theorem.

Lecture 25: Ross Recovery Theorem

This is a guest lecture that describes the HJM model for interest rates and credit, including hedging risk on interest and credit rate derivatives.

Lecture 24: HJM Model for Interest Rates and Credit

This lecture covers the topic of stochastic differential equations, linking probablity theory with ordinary and partial differential equations.

Lecture 21: Stochastic Differential Equations

This guest lecture focuses on option price and probability duality.

Lecture 20: Option Price and Probability Duality

This is a lecture on risk-neutral pricing, featuring the Black-Scholes formula and risk-neutral valuation.

Lecture 19: Black-Scholes Formula, Risk-neutral Valuation

This lecture focuses on portfolio management, including portfolio construction, portfolio theory, risk parity portfolios, and their limitations.

Lecture 16: Portfolio Management

This lecture explains the theory behind Itō calculus.

Lecture 18: Itō Calculus

This lecture covers stochastic processes, including continuous-time stochastic processes and standard Brownian motion.

Lecture 17: Stochastic Processes II

Topics in Mathematics with Applications in Finance

This lecture describes factor modeling, featuring linear, macroeconomic, fundamental, and statistical factor models, and principal components analysis.

Lecture 15: Factor Modeling

This lecture describes portfolio theory, including topics of Marowitz mean-variance optimization, von Neumann-Morganstern utility theory, portfolio optimization constraints, and risk measures.

Lecture 14: Portfolio Theory

This is a guest lecture on commodity modeling, analyzing the methods of generating profit with a constrained system.

Lecture 13: Commodity Models

This is the last of three lectures introducing the topic of time series analysis, describing cointegration, cointegrated VAR models, linear state-space models, and Kalman filters.

Lecture 12: Time Series Analysis III

This is the second of three lectures introducing the topic of time series analysis, describing multivariate time series, representation theorems, and least-squares estimation.

Lecture 11: Time Series Analysis II

This is a guest lecture on regularized pricing and risk models, featuring explanations of bonds, swaps, and yield curve models.

Lecture 10: Regularized Pricing and Risk Models

This lecture introduces the topic of volatility modeling, including historical volatility, geometric Brownian motion, and Poisson jump diffusions.

Lecture 9: Volatility Modeling

This is the first of three lectures introducing the topic of time series analysis, describing stochastic processes by applying regression and stationarity models.

Lecture 8: Time Series Analysis I

This is an applications lecture on Value At Risk (VAR) models, and how financial institutions manage market risk.

Lecture 7: Value At Risk (VAR) Models

This lecture introduces the mathematical and statistical foundations of regression analysis, particularly linear regression.

Lecture 6: Regression Analysis

This lecture is a review of the probability theory needed for the course, including random variables, probability distributions, and the Central Limit Theorem.

Lecture 3: Probability Theory

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