"Having taken many courses so far, Masters of Financial Math (MFM) students have discovered interesting and useful courses. Below are examples of a few core courses I have found important and useful."- Yizhou Chen, May 2015 Graduate
Statistical Theory I & II is important in providing fundamental theory and formulas. In Statistical Theory II, we developed the probabilistic tools and language of mathematical statistics. The course describes basic probability theory, probabilistic models for a properties of random variables, common probability distributions for univariate and multivariate random variables, and sampling distributions and convergence theory. We learn description of discrete and absolutely continuous distributions, expected values, moments, moment generating functions, transformation of random variables, marginal and conditional distributions, independence, order-statistics, multivariate distributions, and concept of random sample.
The Statistical Theory classes are designed to provide the basic tools of statistical inference and prepare us to understand the foundations behind statistical inference. Thus, the knowledge enables us to formulate appropriate statistical procedures. Additionally we learn sufficient, ancillary, and complete statistics; Methods of finding estimators, including maximum likelihood; Mean squared error and unbiasedness; Hypothesis testing, including maximum likelihood; Mean squared error and unbiasedness; Hypothesis testing, including likelihood ratio; Power functions; Neyman-Pearson Lemma; Uniformly most powerful tests; Confidence intervals; Asymptotic properties of estimators and tests.
Asset Pricing is a core course in the first semester of the Financial Math program. We gained a lot knowledge about finance from this course, especially for the students who have little knowledge about finance. This course is an introduction to the pricing of assets. The emphasis is on the mathematical methods used to derive pricing formulas, and there is additional time devoted to explaining the major types of paper assets that can be priced with those methods. Real assets, such as factories and machines, also can be priced with the same methods. The goal of this course is to introduce us to the major types of asset prices and give us an understanding at an intuitive level of the relation between asset prices and the mathematics that governs their evolution.
The content in this course: Introduction to major fundamental assets (stocks and bonds), interest rates, and derivative assets, such as put and call options. Arbitrage theorem, present value, risk aversion, hedging, duration, properties of derivative assets, binomial trees, elementary stochastic calculus, Black-Scholes option pricing formula, implied volatility, capital asset pricing model. Emphasis on mathematical methods used to price derivative assets.
Probability and Stochastic Processes:
Probability and Stochastic Processes I: This course is set as an alternative course to Statistical Theory II. This course is more theoretical and the key point of this course is different from Statistical Theory I. In Statistical Theory I, we developed the probabilistic tools and language of mathematical statistics. Probability and Stochastic Processes describes basic probability theory, probabilistic models for and properties of random variables, common probability distributions for univariate and multivariate random variables, and sampling distributions and convergence theory. It is a modern introduction to Probability Theory and Stochastic Processes. The choice of material is motivated by applications to problems such as queueing networks, filtering and financial mathematics. Topics include: review of discrete probability and continuous random variables, random walks, markov chains, martingales, stopping times, erodicity, conditional expectations, continuous-time Markov chains, laws of large numbers, central limit theorem and large deviations.
Financial Mathematics- This is a core course in second semester, and challenging; some say difficult! Probability and Stochastic Processes and Asset Pricing courses are necessary to prepare us for Financial Mathematics class. Understanding the history of mathematics evolving over time as they are subjected to random shocks and knowledge of the mathematics of asset pricing are essential tools for this course.
Financial Mathematics course focuses on the basic mathematical tools for finance. In particular, we cover time value of the money, simple interest rate, bank discount rates, compound interest, ordinary annuities, extending ordinary annuities, amortization, sinking funds, perpetuities and capitalized costs.
Content of this course: Stochastic models of financial markets, No-arbitrage derivative pricing, discrete to continuous time models, Brownian motion, stochastic calculus, Feynman-Kac formula and tools for European options and equivalent martingale measures. We also learn about Black-Scholes formula, Hedging strategies and management of risk, Optimal stopping and American options, Term structure models and interest rate derivatives, and Stochastic volatility.
Monte Carlo Methods:
Monte Carlo Methods with Application to Financial Mathematics- This course requires some knowledge of programming. We use Matlab to write functions, apply appropriate control structures, and import and export data. We implement the methods mentioned in the other learning outcomes in Matlab. Matlab is utilized to visualize the results. The homework of this course may not be so difficult, but it takes a lot of time. Because of plenty use Matlab, we need take some pre-courses to prepare for it.
In this course we learn Monte Carlo (MC) methods for accurate option pricing, hedging and risk management. Modeling using stochastic asset models (e.g. geometric Brownian motion) and parameter estimation. Stochastic models, including use of random number generators, random paths and discretization methods (e.g. Euler-Maruyama method), and variance reduction."
By- Yizhou Chen, May 2015 Graduate, Career Ambassador & Financial Math Intern
Learn more about NC State Masters of Financial Math.