Description

1. Forwards and futures create obligations; options give buyers the right to buy or sell an underlying asset.

2. Calls give the right to buy, puts the right to sell; European options exercise at maturity, American options also earlier.

3. A bull call spread combines a long lower-strike call with a short higher-strike call, limiting both gains and losses.

4. Butterflies benefit from prices near the middle strike; long straddles and strangles benefit from sufficiently large moves.

5. Payoff describes the terminal contract value; profit also accounts for premiums and, where relevant, financing costs.

6. No-arbitrage pricing links forwards, stocks, bonds, and European options through replication and put–call parity.

7. Binomial models price derivatives by discounting expected payoffs under risk-neutral probabilities.

8. Probability distributions, moments, and dependence underpin financial models; zero covariance does not imply independence.

9. Random walks model discrete price changes, while martingales have conditional expected future values equal to their current values.

10. Brownian motion, Brownian bridges, geometric Brownian motion, and Itô’s lemma provide tools for continuous-time financial modelling.