MIT 18.S096 Topics in Mathematics w Applications in Finance

MIT 18.S096 Topics in Mathematics w Applications in Finance

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