**MIT 18.S096 Topics in Mathematics with Applications in Finance, Fall 2013**

View the complete course: http://ocw.mit.edu/18-S096F13

Instructor: Peter Kempthorne, Choongbum Lee, Vasily Strela, Jake Xia

In the first lecture of this course, the instructors introduce key terms and concepts related to financial products, markets, and quantitative analysis.

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View the complete course: http://ocw.mit.edu/18-S096F13

Instructor: Peter Kempthorne, Choongbum Lee, Vasily Strela, Jake Xia

In the first lecture of this course, the instructors introduce key terms and concepts related to financial products, markets, and quantitative analysis.

License: Creative Commons BY-NC-SA

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**MIT 18.S096 Topics in Mathematics with Applications in Finance, Fall 2013**

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Instructor: Choongbum Lee

This lecture is a review of the linear algebra needed for the course, including matrices, linear transformations, eigenvalue, and eigenvectors.

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Instructor: Choongbum Lee

This lecture is a review of the linear algebra needed for the course, including matrices, linear transformations, eigenvalue, and eigenvectors.

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**MIT 18.S096 Topics in Mathematics with Applications in Finance, Fall 2013**

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Instructor: Choongbum Lee

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.

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Instructor: Choongbum Lee

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.

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**MIT 18.S096 Topics in Mathematics with Applications in Finance, Fall 2013**

View the complete course: http://ocw.mit.edu/18-S096F13

Instructor: Choongbum Lee

*NOTE: Lecture 4 was not recorded.

This lecture introduces stochastic processes, including random walks and Markov chains.

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Instructor: Choongbum Lee

*NOTE: Lecture 4 was not recorded.

This lecture introduces stochastic processes, including random walks and Markov chains.

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**MIT 18.S096 Topics in Mathematics with Applications in Finance, Fall 2013**

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Instructor: Peter Kempthorne

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

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Instructor: Peter Kempthorne

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

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**MIT 18.S096 Topics in Mathematics with Applications in Finance, Fall 2013**

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Instructor: Kenneth Abbott

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

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Instructor: Kenneth Abbott

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

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**MIT 18.S096 Topics in Mathematics with Applications in Finance, Fall 2013**

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Instructor: Peter Kempthorne

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

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Instructor: Peter Kempthorne

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

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**MIT 18.S096 Topics in Mathematics with Applications in Finance, Fall 2013**

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Instructor: Peter Kempthorne

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

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Instructor: Peter Kempthorne

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

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**MIT 18.S096 Topics in Mathematics with Applications in Finance, Fall 2013**

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Instructor: Ivan Masyukov

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

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Instructor: Ivan Masyukov

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

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**MIT 18.S096 Topics in Mathematics with Applications in Finance, Fall 2013**

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Instructor: Peter Kempthorne

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

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Instructor: Peter Kempthorne

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

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**MIT 18.S096 Topics in Mathematics with Applications in Finance, Fall 2013**

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Instructor: Peter Kempthorne

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.

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Instructor: Peter Kempthorne

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.

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**MIT 18.S096 Topics in Mathematics with Applications in Finance, Fall 2013**

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Instructor: Alexander Eydeland

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

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Instructor: Alexander Eydeland

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

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**MIT 18.S096 Topics in Mathematics with Applications in Finance, Fall 2013**

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Instructor: Peter Kempthorne

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

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Instructor: Peter Kempthorne

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

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**MIT 18.S096 Topics in Mathematics with Applications in Finance, Fall 2013**

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Instructor: Peter Kempthorne

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

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Instructor: Peter Kempthorne

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

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**MIT 18.S096 Topics in Mathematics with Applications in Finance, Fall 2013**

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Instructor: Jake Xia

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

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Instructor: Jake Xia

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

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**MIT 18.S096 Topics in Mathematics with Applications in Finance, Fall 2013**

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Instructor: Choongbum Lee

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

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Instructor: Choongbum Lee

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

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**MIT 18.S096 Topics in Mathematics with Applications in Finance, Fall 2013**

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Instructor: Choongbum Lee

This lecture explains the theory behind Itoíã calculus.

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Instructor: Choongbum Lee

This lecture explains the theory behind Itoíã calculus.

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**MIT 18.S096 Topics in Mathematics with Applications in Finance, Fall 2013**

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Instructor: Vasily Strela

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

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Instructor: Vasily Strela

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

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**MIT 18.S096 Topics in Mathematics with Applications in Finance, Fall 2013**

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Instructor: Stephen Blythe

This guest lecture focuses on option price and probability duality.

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Instructor: Stephen Blythe

This guest lecture focuses on option price and probability duality.

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**MIT 18.S096 Topics in Mathematics with Applications in Finance, Fall 2013**

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Instructor: Choongbum Lee

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

00:21 – Stochastic Differential Equations

21:15 – Numerical methods

42:27 – Heat Equation

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Instructor: Choongbum Lee

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

00:21 – Stochastic Differential Equations

21:15 – Numerical methods

42:27 – Heat Equation

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**MIT 18.S096 Topics in Mathematics with Applications in Finance, Fall 2013**

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Instructor: Stefan Andreev

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

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Instructor: Stefan Andreev

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

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**MIT 18.S096 Topics in Mathematics with Applications in Finance, Fall 2013**

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Instructor: Denis Gorokhov

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

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Instructor: Denis Gorokhov

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

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**MIT 18.S096 Topics in Mathematics with Applications in Finance, Fall 2013**

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Instructor: Peter Carr

This guest lecture features the Ross Recovery Theorem.

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Instructor: Peter Carr

This guest lecture features the Ross Recovery Theorem.

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**MIT 18.S096 Topics in Mathematics with Applications in Finance, Fall 2013**

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Instructor: Yi Tang

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.

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Instructor: Yi Tang

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.

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