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Financial Mathematics
The course consists of two components.The first component concentrates on topics in time series econometrics, which may include • univariate nonlinear stochastic models; stationary nonlinear models; nonlinear time series models; regression analysis of time series;• discrete and continuous time series with long-range dependence. Applications include risk management and term structure dynamics, nonlinear estimation of interest rate models and nonparametric pricing• derivatives, selection of time series models for detecting climate change, and trend detection in regional mean temperature series.Regarding the second, topics will be selected from: • Discrete time models I (Single period models, pricing a European option, characterizing no arbitrage, risk neutral probabilities);• Discrete time models II (Multiperiod binary models, discrete parameter martingales, risk-neutral pricing, Cox-Ross-Rubinstein);• Brownian motion (Definition and Lévy's construction); The reflection principle and hitting times (reflection principle, hitting times, scaling properties);• Martingales in continuous time (filtrations, adapted processes, Optional Sampling Theorem);• Stochastic integration and Ito's formula; The Martingale Representation Theorem, Lévy's characterisation of Brownian motion, Girsanov's Theorem;• The Black-Scholes model; Pricing and hedging European options; Evaluation of price and hedging strategies for European calls and puts.
Subject to approval of the Head of School.
Patrick W Saart
MATH408 Homepage Mathematics and Statistics Honours Booklet
Domestic fee $788.00
International Postgraduate fees
* All fees are inclusive of NZ GST or any equivalent overseas tax, and do not include any programme level discount or additional course-related expenses.
For further information see Mathematics and Statistics .