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# Applied Mathematics & Statistics

AMS 511, Foundation of Quantitative Finance
Introduction to capital markets, securities pricing, and modern portfolio theory, including the organization and operation of securities market, the Efficient Market Hypothesis and its implications, the Capital Asset Pricing Model, the Arbitrage Pricing Theory, and more general factor models. Common stocks and their valuation, statistical analysis, and portfolio selection in a single-period, mean-variance context will be explored along with its solution as a quadratic program. Fixed income securities and their valuation, statistical analysis, and portfolio selection. Discussion of the development and use of financial derivatives. Introduction to risk neutral pricing, stochastic calculus, and the Black-Scholes Formula. Whenever practical, examples will use real market data. Numerical exercises and projects in a high-level programming environment will also be assigned.

Prerequisite:  AMS 505 or  510

Course Materials  for Fall 2017:
"Investment Science" by David G. Luenberger, 2nd edition, Oxford University Press, 2014; ISBN 9780-19-974008-6

Learning Outcomes:

1.) Understand the function of the financial industry as an economic section and the main components of financial markets.
* Financial assets;
* Financial intermediaries;
* Regulations on financial markets.

2.) Evaluate the value of simple fixed-income securities and understand the mechanics of complicated fixed-income securities.
* Evaluation of bond value;
* Yield curve and spot rate;
* Collateralized debt obligation (CDO) and credit default swap (CDS).

3.) Evaluate to evaluation the value of risky securities using the arbitrage pricing theory (APT) and the Black-Schole’s formula.
* Arbitrage-free in one-period discrete model;
* Continuous model and Black-Schole’s formula;

4.) Understand the concepts in modern portfolio theory and capital asset pricing model (CAPM).
* Utility, risk and return of investments;
* Mutual fund theorem;
* Separation theorem.

5.) Understand the importance of regulation and risk management for financial agents.
* Government regulation and the 2010 financial reforms;
* Measuring risk exposures;
* Stress testing.

6.) Demonstrate skill with mathematical and statistical methods used in financial analytics. 