Curriculum

Application of finance theory to careers in finance; development of practical skills for finance professionals, including proficiency with industry-standard software, databases and analytic products; operational, legal and ethical aspects of the financial industry; financial career planning.

Theoretical development and application of principles of investment management; topics include measuring risk aversion, portfolio optimization, factor models, asset pricing models, bond pricing, term structure of interest rates, bend portfolio management and equity valuation.

Analytical, numerical, and statistical methods used in quantitative finance research. These methods are used to price various financial assets, manage the portfolios of those securities, evaluate performances of various financial strategies, and study various economic decision making. The course provides students with a deep understanding of dynamic stochastic asset pricing models and related optimal decision making of various stakeholders, including corporation and fund-managing institutions.

Quantitative tools designed to price and hedge derivative securities and to employ quantitative risk management techniques. Martingales, quadratic variation process, Itô integrals and processes, Brownian motion, geometric Brownian motion, Ornstein-Uhlenbeck process, Girsanov’s theorem, and Feynman-Kac formula. Modeling of asset return dynamics and and self-financing portfolios. Use of the stochastic discount factor (SDF) to price stocks, bonds, foreign currencies, forwards, futures, swaps, and options. Relation between the SDF, the fundamental partial differential equation, and the risk-neutral valuation approach in derivative pricing. Applications to hedging in the equity, treasury, energy, and foreign exchange markets. Value-at-Risk (VaR) concepts.

Advanced topics in financial economics and institutions related to bond markets and the determinants of price and interest rate (yield) for fixed income securities, including Treasury issues, federal agency issues, corporate bonds, municipal bonds, mortgage-backed and asset-backed securities. Topics include i) features of fixed income securities (microeconomic and macroeconomic perspectives), ii) risks and uncertainties of bond investing, iii) fixed income valuation, iv) term structure and credit structure models of fixed income securities, and v) trading strategies and risk management using fixed income strategies.

Pricing of financial derivatives in different market models; discrete models: Arrow-Debreu, Binomial model, Hedging; Stochastic calculus; Brownian Motion, stochastic integrals, Ito formula; continuous model: Black-Scholes formula for pricing European and American options; equivalent Martingale Measures, pricing of exotic options.

Stochastic Calculus. Topics include Brownian motion, Ito integrals, Ito formula, Martingale Theorem, stochastic differential equations, Feynman-Kac Formula, Random time change, Girsanov theorem, and application to mathematical finance.

Asset returns, fixed income securities, exploratory data analysis, modeling univariate distribution, multivariate statistical models, copulas, portfolio selection, risk management, the capital asset pricing model, factor models and principal components, time series models, GARCH models.