8 - 12 January 2018
- Probability: Axiomatic approach to probability, random variables, expectation and integration, multidimensional random variables (and independence), conditional expectation, convergence of random variables;
- PDEs: parabolic partial differential equations, heat equation, link to random walks, similarity solutions, Fourier transform; qualitative properties of solutions, maximum principles, smoothness;
- Applied Stochastic Calculus: Brownian motion, constructions, non-differentiability, quadratic variation, stochastic integration, construction of Ito integral and properties, the Ito formula, Feynman-Kac formula;
- Statistics: basic parameter estimation, maximum likelihood estimation, distributions, regression techniques, tests for normality, QQ plots, hypothesis testing, numberical examples in R
- Binomial trees, discrete martingales: simple random walk, change of measure, one-period and multi-period binomial stock price models, arbitrage-pricing of options on trees;
- Portfolio theory, utility: expected returns, variance and covariances, benefits of diversification, the opportunity set, efficient frontiers and the Sharpe ratio, utility, risk aversion, and
- Introduction to Matlab: basics, plotting, implementation of elementary numerical concepts applied to finance.
Assignment due: 12 noon UK time, 12 February 2018
The Module 1 assignment is available under Course Materials during, or shortly after, the week you are in Oxford. Although not a compulsory assignment, it is highly recommended that you do submit an assignment to give an indication of how you are progressing on the course, ready for the examinations. If you do not plan to submit the assignment then please let the Course Administrator know.
Keep a record of the submission ID for future reference. If you encounter any problems please contact the Course Administrator as soon as possible.
Please remember to put your candidate number, rather than your name, on the assignment. You can find your candidate number on the Student Self Service System.