STATS 723 Stochastic Methods in Finance

Below description edited in year: 2010

Points: 15

Prereqs: STATS 210 or equivalent, or consent of lecturer.

Credit: Final exam = 75%, assignments = 25%; or final exam = 100%

Textbooks: N. Bingham and R. Kiesel, "Risk-neutral valuation - pricing and hedging of financial derivatives". L. Clewlow and C. Strickland, "Implementing derivatives models".

For Advice: Geoffrey Pritchard (Email: g.pritchard@auckland.ac.nz | extn: 87400)

Taught: First Semester City

STATS 723 is a course in mathematical finance. We will use the techniques of probability and stochastic processes to study derivative securities that are traded in financial markets. The course is suitable for students of statistics, finance, accounting, economics, or mathematics.

Topics studied include: Probability and background - Random variables, distributions, equivalent measures. Essential notions - financial derivatives, arbitrage, replicating portfolios, risk-neutral pricing, complete markets. Martingales. Mathematical finance in discrete time -equivalent martingale measures, Fundamental Theorem of Asset Pricing, Cox-Ross-Rubinstein model. Option pricing, including path-dependent options. Continuous-time stochastic processes - Brownian motion, stochastic integral, Ito's lemma, stochastic differential equations. Mathematical finance in continuous time - Fundamental Theorem of Asset Pricing in continuous time. The Black-Scholes world. Hedge sensitivities ("Greeks"). Further topics - a selection from: volatility estimation, volatility smiles; risk management and hedging, risk measures (VaR and CVaR); multi-factor and other models, Monte Carlo simulation; incomplete markets.

Disclaimer:
Although every reasonable effort is made to ensure accuracy, this information for the course year (2011), 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.