| Topic | References |
|---|---|
| Introduction to the course | Browse in S&P guide (sections on money, stocks, and options) |
| The motion of stock prices, return and log return | - |
| Discrete and continuous compound interest; present and future value | Hull 4.1, 4.2; also any calculus book |
| Random variables, expectation, variance, the normal distribution | - |
| Brownian motion as limit of coin tossing (random walk). Geometric Brownian motion. | Handouts, also Hull 12.1--12.4 |
| Normality and independence of returns as a consequence of GBM | - |
| Sample mean, variance, standard deviation, confidence intervals | - |
| Tests for normality: KS test, qq-plot | - |
| Analyse stock data using SPSS; estimating the parameters in GBM | - |
| Simulating GBM using Excel | Handout |
| Covarience, correlation | - |
| Tests for independence: scatterplot, sample correlation coefficient | - |
| Market portfolio, indices (eg Dow-Jones, S&P 500) | - |
| Forwards | Hull 1.3 |
| Futures | Hull 1.4, also S&P guide |
| Introduction to options: long and short european puts and calls | Hull 1.5 |
| Bachelier (payoff) diagrams | - |
| Put-call parity | Hull 9.4 |
| One-step binomial trees | Hull Ch. 11 |
| Risk-neutral valuation | Hull 11.2 |
| Two-step binomial trees | Hull 11.3 |
| Multi-step binomial trees and Derivagem | 11.8 |
| From trees to the BS formula | Handout |
| Black-Scholes formula | Hull 13.8 |
| Stochastic calculus, Ito's lemma | Hull 13.5 |
| Black-Scholes PDE | Hull 13.6 |
| American options, evaluation with a tree | Hull 11.5 |
| Comparing actual option prices with their BS values; implied volatility, volatility smiles | Hull 13.11 |
| The Greeks | Hull Ch. 15 |
| Exotic options | Hull Ch. 22 |
| Monte Carlo methods | Hull 17.6 |