STATS 722 Financial Mathematics

Below description edited in year: 2013

Points: 15

Prereqs: 15 points in Stage 2 Statistics and 15 points in Stage 2 Mathematics

Restrictions: STATS 370

Credit: Final exam 80%; coursework 20%

Textbooks: None. Handouts will be given out

For Advice: Robert Chan (Email: chan [@] math.auckland.ac.nz | extn: 85212)

Taught: Second Semester City

Website: STATS 722 website

This course includes the material in STATS 370. It is intended for postgraduate students who have not already passed STATS 370.

STATS 722 is an extended version of STATS 370. It uses mathematical, statistical and stochastic methods in finance. It covers mean-variance portfolio theory, interest rate theory, basic derivative securities including the derivation of the Black-Scholes option pricing formula, and hedging strategies. The course is suitable for students of statistics, finance, accounting, economics or mathematics.

Topics studied include:Basic probability, investment portfolios, mean, variance and covariance of returns, minimum variance portfolio, portfolio possibilities regions and their properties, the efficient portfolio frontier, riskless lending and borrowing, short sales, single index structural models. An introduction to stochastic differential equations and their solution, simple and compound interest, effective and nominal interest rates, accumulation factors, force of interest, equivalent interest rates, present value, basic compound interest functions, equation of value for a sequence of transactions, internal rate of return, annuities, loan schedules. Stocks, futures contracts, European and American call and put options, arbitrage, Brownian motion, Ito processes, Ito’s lemma, geometric Brownian motion, put-call relationships, Black-Scholes analysis and pricing formulae, risk-neutral valuation, pricing American options, the Cox-Ross-Rubinstein binomial model for stock prices.

Disclaimer:
Although every reasonable effort is made to ensure accuracy, this information for the course year (2013), is provided as a general guide only for students and is subject to alteration. All students enrolling at the University of Auckland must consult its official document, the University of Auckland Calendar, to ensure that they are aware of and comply with all regulations, requirements and policies.