Topics in Mathematics with Applications in Finance

Video Lectures

Displaying all 26 video lectures.
Lecture 1
Introduction, Financial Terms and Concepts
Play Video		 Introduction, Financial Terms and Concepts
In the first lecture of this course, the instructors introduce key terms and concepts related to financial products, markets, and quantitative analysis.

Instructor: Peter Kempthorne, Choongbum Lee, Vasily Strela, Jake Xia
Lecture 2
Linear Algebra
Play Video		 Linear Algebra
This lecture is a review of the linear algebra needed for the course, including matrices, linear transformations, eigenvalue, and eigenvectors.

Instructor: Choongbum Lee
Lecture 3
Probability Theory
Play Video		 Probability Theory
This lecture is a review of the probability theory needed for the course, including random variables, probability distributions, and the Central Limit Theorem.

*NOTE: Lecture 4 was not recorded.

Instructor: Choongbum Lee
Lecture 4
Unavailable
Play Video		 Unavailable
Lecture 5
Stochastic Processes I
Play Video		 Stochastic Processes I
Instructor: Choongbum Lee

*NOTE: Lecture 4 was not recorded.
This lecture introduces stochastic processes, including random walks and Markov chains.
Lecture 6
Regression Analysis
Play Video		 Regression Analysis
This lecture introduces the mathematical and statistical foundations of regression analysis, particularly linear regression.

Instructor: Peter Kempthorne
Lecture 7
Value At Risk (VAR) Models
Play Video		 Value At Risk (VAR) Models
This is an applications lecture on Value At Risk (VAR) models, and how financial institutions manage market risk.

Instructor: Kenneth Abbott
Lecture 8
Time Series Analysis I
Play Video		 Time Series Analysis I
This is the first of three lectures introducing the topic of time series analysis, describing stochastic processes by applying regression and stationarity models.

Instructor: Peter Kempthorne
Lecture 9
Volatility Modeling
Play Video		 Volatility Modeling
This lecture introduces the topic of volatility modeling, including historical volatility, geometric Brownian motion, and Poisson jump diffusions.

Instructor: Peter Kempthorne
Lecture 10
Regularized Pricing and Risk Models
Play Video		 Regularized Pricing and Risk Models
This is a guest lecture on regularized pricing and risk models, featuring explanations of bonds, swaps, and yield curve models.

Instructor: Ivan Masyukov
Lecture 11
Time Series Analysis II
Play Video		 Time Series Analysis II
This is the second of three lectures introducing the topic of time series analysis, describing multivariate time series, representation theorems, and least-squares estimation.

Instructor: Peter Kempthorne
Lecture 12
Time Series Analysis III
Play Video		 Time Series Analysis III
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.

Instructor: Peter Kempthorne
Lecture 13
Commodity Models
Play Video		 Commodity Models
This is a guest lecture on commodity modeling, analyzing the methods of generating profit with a constrained system.

Instructor: Alexander Eydeland
Lecture 14
Portfolio Theory
Play Video		 Portfolio Theory
This lecture describes portfolio theory, including topics of Marowitz mean-variance optimization, von Neumann-Morganstern utility theory, portfolio optimization constraints, and risk measures.

Instructor: Peter Kempthorne
Lecture 15
Factor Modeling
Play Video		 Factor Modeling
This lecture describes factor modeling, featuring linear, macroeconomic, fundamental, and statistical factor models, and principal components analysis.

Instructor: Peter Kempthorne
Lecture 16
Portfolio Management
Play Video		 Portfolio Management
This lecture focuses on portfolio management, including portfolio construction, portfolio theory, risk parity portfolios, and their limitations.

Instructor: Jake Xia
Lecture 17
Stochastic Processes II
Play Video		 Stochastic Processes II
This lecture covers stochastic processes, including continuous-time stochastic processes and standard Brownian motion.

Instructor: Choongbum Lee
Lecture 18
Itō Calculus
Play Video		 Itō Calculus
This lecture explains the theory behind Itō calculus.

Instructor: Choongbum Lee
Lecture 19
Black-Scholes Formula, Risk-neutral Valuation
Play Video		 Black-Scholes Formula, Risk-neutral Valuation
This is a lecture on risk-neutral pricing, featuring the Black-Scholes formula and risk-neutral valuation.

Instructor: Vasily Strela
Lecture 20
Option Price and Probability Duality
Play Video		 Option Price and Probability Duality
This guest lecture focuses on option price and probability duality.

Instructor: Stephen Blythe
Lecture 21
Stochastic Differential Equations
Play Video		 Stochastic Differential Equations
This lecture covers the topic of stochastic differential equations, linking probablity theory with ordinary and partial differential equations.

Instructor: Choongbum Lee
Lecture 22
Unavailable
Play Video		 Unavailable
Lecture 23
Quanto Credit Hedging
Play Video		 Quanto Credit Hedging
This is a guest lecture on quanto credit hedging, including using mathematical models in trading.

Instructor: Stefan Andreev
Lecture 24
HJM Model for Interest Rates and Credit
Play Video		 HJM Model for Interest Rates and Credit
This is a guest lecture that describes the HJM model for interest rates and credit, including hedging risk on interest and credit rate derivatives.

Instructor: Denis Gorokhov
Lecture 25
Ross Recovery Theorem
Play Video		 Ross Recovery Theorem
This guest lecture features the Ross Recovery Theorem.

Instructor: Peter Carr
Lecture 26
Introduction to Counterparty Credit Risk
Play Video		 Introduction to Counterparty Credit Risk
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.

Instructor: Yi Tang