Topics in Mathematics with Applications in Finance

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

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

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

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

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

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

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

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

This lecture explores regularized pricing and risk models, detailing their application to bond valuation, swap pricing, and the construction of robust yield curve models in financial markets.

This session continues time series analysis, covering multivariate time series representations, fundamental representation theorems, and the theory of least-squares estimation for financial data.

The final time series lecture examines cointegration, integrating VAR models, linear state-space models, and the Kalman filter for analyzing long-run economic relationships.

This lecture delves into commodity modeling, presenting various methodologies for generating profit within constrained systems, specifically tailored for commodity markets and their unique dynamics.

This lecture introduces modern portfolio theory, discussing Marowitz mean-variance optimization, von Neumann-Morganstern utility theory, portfolio optimization constraints, and various risk measures.

This lecture explores factor modeling, detailing linear, macroeconomic, fundamental, and statistical factor models, alongside an introduction to principal components analysis for risk attribution.

This lecture focuses on advanced portfolio management, covering portfolio construction techniques, extensions of portfolio theory, the concept of risk parity portfolios, and their inherent limitations.

This lecture expands on stochastic processes, specifically covering continuous-time stochastic processes and providing a detailed analysis of standard Brownian motion, a cornerstone in quantitative finance.

This lecture provides a rigorous explanation of Itō calculus, elucidating its fundamental theorems and applications in the context of stochastic differential equations crucial for financial modeling.

This lecture introduces risk-neutral pricing, deriving the Black-Scholes formula and explaining its principles for valuing options through the fundamental concept of risk-neutral valuation.

This guest lecture examines the profound duality between option prices and probabilities, illustrating how these seemingly distinct concepts are intrinsically linked within financial mathematics.

This lecture explores stochastic differential equations, connecting probability theory with ordinary and partial differential equations, and introduces numerical methods and the heat equation.

This guest lecture focuses on quanto credit hedging, demonstrating how mathematical models are applied in sophisticated trading strategies to manage complex cross-currency and credit risks.

This lecture introduces the Heath-Jarrow-Morton (HJM) model for interest rates and credit, covering its application in hedging risk on interest and credit rate derivatives through no-arbitrage pricing.