i. Introduction to various forms of investment. Risk and return.
ii. Interest rates: risk-free, cumulative, compound. Depreciation.
iii. Share prices as quantities with a deterministic and random component. Drift, volatility and interest rate.
iv. Random variables; density and distribution functions. Some common density functions such as
, binomial & Poisson. The Levy distribution as a generalised distribution with improved representation of rare events.
v. Methods for calculating the volatility (risk) of a stock.
vi. European put and call options and their use to reduce risk or as a speculative investment. Introduction to American options and covered warrants. Put-call parity. Interpreting information in the Financial Times.
vii. The binomial tree as a model for pricing European and American options. Implementation of the one-step, two-step and multi-step models in practice.
viii. Ito’s Lemma (
’s theorem for random variables). The lognormal density function.
ix. Derivation of the Black-Scholes equation for the value of an option. Arbitrage and delta hedging. Reduction to a diffusion equation. Solution of the Black-Scholes equation for European calls and puts. Implied volatility.
x. The perpetual American put.
xi. The Greeks.