Topics in Mathematics with Applications in Finance

Video Lectures

Displaying all 26 video lectures.
Lecture 1
Introduction, Financial Terms and Concepts
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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
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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
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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
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Lecture 5
Stochastic Processes I
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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Stochastic Processes II
This lecture covers stochastic processes, including continuous-time stochastic processes and standard Brownian motion.

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

Instructor: Choongbum Lee
Lecture 19
Black-Scholes Formula, Risk-neutral Valuation
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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
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Option Price and Probability Duality
This guest lecture focuses on option price and probability duality.

Instructor: Stephen Blythe
Lecture 21
Stochastic Differential Equations
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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
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Lecture 23
Quanto Credit Hedging
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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
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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
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Ross Recovery Theorem
This guest lecture features the Ross Recovery Theorem.

Instructor: Peter Carr
Lecture 26
Introduction to Counterparty Credit Risk
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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