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Department:

MATH

Course Number:

6759

Hours - Lecture:

3

Hours - Lab:

0

Hours - Recitation:

0

Hours - Total Credit:

3

Typical Scheduling:

Every fall semester (ISyE)

Mathematical modeling of financial markets, derivative securities pricing, and portfolio optimization. Concepts from probability and mathematics are introduced as needed. Crosslisted with ISYE 6759.

Prerequisites:

MATH 3215 and some knowledge of computer programming

Course Text:

Class notes are used for this course; these notes are at the level of *Introduction to Mathematical Finance: Discrete Time Models* by S. Pliska, published by Blackwell Publishers

Topic Outline:

- Discussion of prerequisites, including basic probability background and linear systems of equations
- Some probability background, including Riemann-Stieltjes integrals and conditional probabilities and conditional expectations. Definitions of some financial terms.
- The Binomial Market Model and its use in pricing and hedging claims. European style options, some exotic options.
- Model implementation, implied volatility. Probability background: convergence in distribution, and a central limit theorem
- Convergence of Binomial option prices to Black-Scholes option prices, and a sketch of the Black-Scholes Market Model
- Use of derivative securities, and strategies for trading. The greeks, and their use in option trading.
- Probability and mathematics background: martingales, separating hyperplanes, linear programming and duality
- The Discrete-time, Stochastic Market Model, conditions of no-arbitrage and completeness, and pricing and hedging claims
- Variations of the basic models: American style options, foreign exchange derivatives, derivatives on stocks paying dividends, and forward prices and futures prices
- Probability background: Markov chains. Stochastic volatility and implied trees.
- Stochastic interest rates, bonds and interest rate derivatives. Model implementation.
- Mathematical background: optimization techniques. Incomplete Market Models. Utility-based pricing in complete markets and in incomplete markets. Portfolio optimization