This note introduces the contracts we will spend the whole course pricing, and shows how far we can get without any model at all. Remarkably far, it turns out: from the single assumption that risk-free profits above the bank rate are impossible, we obtain hard bounds on option values, the put–call parity identity, and the inequality between American and European prices. Everything here is model-free — it must hold no matter which stochastic process we later choose for the stock.
Learning objectives. By the end of this note you should be able to:
- define call/put options and the European/American/Bermudan/barrier exercise styles;
- write down payoff functions and explain their computational role as terminal conditions;
- state and prove the a priori bounds using explicit arbitrage strategies;
- derive put–call parity from a two-portfolio comparison and use it in pricing questions.
In this lesson
- 1.1 What is an option?
- 1.2 Payoff functions and terminal conditions
- 1.3 A priori bounds and no-arbitrage intuition
- 1.4 Put–call parity
The full lesson, with worked examples and exercise solutions, is for members.
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