Statistical and Applied Mathematical Sciences Institute
19 T. W. Alexander Drive
P.O. Box 14006
Research Triangle Park, NC 27709-4006
Tel: 919.685.9350 FAX: 919.685.9360
[email protected]

SAMSI course on 

"Special Topics in Financial Mathematics"

Instructors:

Jean-Pierre Fouque, Department of Mathematics -  North Carolina State University

Paul Fackler, Agricultural and Resource Economics - North Carolina State University

Ronnie Sircar, Operations Research and Financial Engineering - Princeton University 

Class Time:  Wednesdays, 4:30-7:00pm

Class Location:  NISS Building, Room 104 (directions)

Class begins August 31, 2005

University Listings

Duke                     STA 294.02

NC State               ECG 790M.001, MA 797M.001, ST 810M.001

UNC                     MATH 390.55

COURSE INFORMATION

The course will start by a review of no-arbitrage pricing in complete and incomplete markets in continuous time in the context of equity, fixed income, and credits markets.  Stochastic volatility models and implied volatility smiles an skews will be introduced.  Derivative pricing & hedging when volatility is uncertain will be treated in the context of multiscale modeling with asymptotic methods.

The second part of the course is devoted to real option modeling. Real options arise when decision makers can choose among a set of mutually exclusive activities. The option to switch out of a current activity can be valued by solving an optimal switching problem. Such models arise in numerous situations, including American option pricing problems, entry/exit problems, sequential choice problems, job change problems and many more. This course will discuss the general decision problem in which real options arise and computational techniques for solving such problems. Examples from the literature will be used to illustrate and motivate the discussion. In addition covering the one state models that represent the bulk of current applications, recent innovations in formulating and solving multi-state problems will be discussed.

In the last part of the course optimal hedging and risk management problems involving derivatives will be studied.

Prerequisites: a first graduate course in financial mathematics such as MA 547 offered at NC State (or equivalent)

Reading Materials from Paul Fackler

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