Module 1: Mathematical and Technical Prerequisites

The next course will take place: Monday 7 - Friday 11 January 2019

 

Syllabus

  • 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, similarity solutions, Fourier transforms;
  • Applied Stochastic Calculus: Brownian motion, constructions, non-differentiability, quadratic variation, stochastic integration, construction of Itô integral and properties, the Itô's formula, Feynman-Kac formula;
  • Statistics: basic parameter estimation, maximum likelihood estimation, distributions, regression techniques, tests for normality, QQ plots, hypothesis testing, numberical examples in Python;
  • 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;
  • Utility and Portfolio Theory: utility functions and CAPM formulations; and
  • Introduction to Python: basics, plotting, implementation of elementary numerical concepts applied to finance.

 

For students enrolled on course

Course Materials - including student instructions, lecture notes, assignment and submission link