3. The classical theory of option pricing

‘The classical theory of option pricing’ explains the theory of arbitrage pricing, which is closely related to the Dutch Book Arguments, but which brings in a new factor: prices in financial markets evolve over time and participants are able to trade at any time, instead of just taking bets and awaiting the result. In addition to the general theory, pricing models and methods have been developed for specific markets—foreign exchange, interest rates, and credit. The binomial and continuous-time mathematical models for stock prices are introduced along with the Black–Scholes formula, the volatility surface, the difference between European and American options, and the Fundamental Theorem of Asset Pricing.